Weird cards to consider: Instants and Sorceries - Part 1 (All)

 A few quick gatherer searches and some filtering (Incite != good) gives us around 20 cards that could potentially be useful for the Pyromancer Ascension decklist, that work "inside" the existing strategy, by being instants or sorceries.  They can charge up the Ascension, be doubled by it, and generally work with the existing strategy, but they also tend to be countered by the same things that counter the original strategy.  Hate cards like Negate, Kor Firewalker, and Spell Pierce counter them just as well as they counter the spells you are already using.

So, by no means is this necessarily the "best" strategy to use for "alternative" cards, it is just one category, that is fairly easy to explore.  So lets explore it, and see if anything interesting falls out.

Counterspells:

Counters anything.  Very useful to have a general-purpose counter against multi-threat decks like Valakut Ramp (Summoning Trap, Primeval Titan, both need to be hard-countered), or control decks(Titans, Planeswalkers are critical to stop).  Downside is, of course, mana cost.  You might not have three mana open, or six to pay for the Mana Leak response, when the opposition goes for their ramp-aided Jace, Titan, or Trap.

Counters things that kill PA, unless those things are Ratchet Bomb, Acidic Slime, Ulamog, War Priest of Thune, Luminarchs Ascension, Leyline of Sanctity, Argentum Armor, Negate, Mana Leak, Spell Pierce, Flashfreeze, ...
It does counter Nature's Claim, Celestial Purge, Revoke Existance, Into the Roil, and maybe some other spells that aren't legal in standard.
Coincidentally, Negate counters probably half of the other things that Turn Aside doesn't counter.  It does cost one more mana, which is relevant, but probably not enough to make Turn Aside take up sideboard slots.

Counters anything (like Cancel), counters "uncounterable" things (like Emrakul, Gaea's Revenge), doesn't trigger summoning trap (which offsets the high cost - you won't need to have a counter for the summoning trap this turn), as well as countering summoning trap #1-2 for free, depending on how the turn went.  It also prevents recursion via Emeria, Sun Titan, or Eldrazi shuffle effects.

If Cancel is a good idea, because it's a general answer to things like Titans, Planeswalkers, or such that Negate or Flashfreeze can't generally answer, Mindbreak Trap just seems like a better answer.  The casting cost difference won't be a big deal (because you're countering expensive spells).
This is definately worth considering.

Counters alot of things you care about.  Planeswalkers, counterspells, many of the answers to Ascension.  It is also pretty good lategame, where your opponent casts a Jace on 9 mana or something.

It has some problems though.  Against control, it counters their ramp, draw, and counterspells, but they just cast a Frost Titan, and you die.  Against ramp, it counters SOME of their ramp (not Treespeaker, Battlement), but it doesn't counter the matchup-defining spell (Primeval Titan).
Negate is a top-5 counterspell to be sure, but it may just not counter enough to beat out Mindbreak Trap, Flashfreeze, and Cancel.

Burn:

Competes with Pyroclasm.  You have no creatures to kill when you bring this in (It and Kiln Fiend work at cross purposes), and killing n 2-toughness creatures is better than killing a 2 toughness and a 1 toughness.  Becomes slightly less dead when doubled, as it can take down mana-walls, or bigger guys.  Pyroclasm also doesn't target, for Frost Titan concerns.  Arc Trail does go to the face though, which is something.  It may be better to main 2x Arc Trail, and sideboard the Pyroclasms, since Arc Trail is never truly dead.  And once the board has stabilized, Arc Trail is definately better than Pyroclasm.

Staggershock is better than Arc Trail, for this deck, but the question is whether Arc Trail is better than Pyroclasm for the sideboard.

Forked bolt does the same 2 to them as Arc Trail, but in the end, this seems worse than Staggershock and Arc Trail.

If only it could kill Kor Firewalker...

Would be best as a 1-2-of, which is not great in general for this deck.

4 damage for 3 mana is relevant compared to Burst Lightning as a pure burn spell.  It is potential card advantage against aggro, and a wincondition with the decks general strategy.
See Surreal Memoir for rebound discussion.
Could replace Pyroclasm maindeck, or compete with Arc Trail for sideboard space.
Staggershock is a pretty awesome general answer spell, so it really deserves consideration.

Draw:

A red version of call to mind, that is always ascended (good), but only returns instants, not sorceries, which is probably bad.  The instant-speed targets in this deck are:Countermagic:  will tend to be bad, because it is of "pay x more" variety, which becomes less relevant as the game goes on.
Burn: Would be good in the "kill them out" stage.  Presuming we get there.
Utility: Into the Roil, Twitch, etc.

Ascended rebound spells get four total copies, but not because the first copy rebounds.  The second copy is also "cast", so it triggers the ascension copy.  The rebound on the first copy is not triggered, because the copy is not cast "from your hand".  So you do get a doubled spell, for four total copies.  If you have an additional copy of the rebound spell in your graveyard, the rebound will fully charge your PA up, but if you don't, you will get 0 counters from the original + rebound (because the card is not in your graveyard to see itself on the rebound)

Notably absent from this list is any of the card drawing, which is what you tend to want to draw when you're ascended with 7-9 mana out, trying to find a way to take advantage of the stalled board state.
The EV of this card goes up quite a bit as the red spell count increases, and the blue spell count decreases, since the "just kill them" plan becomes more plausible, and Surreal Memoir becomes a mini-ascension when you either don't get it online, or whatever.

A good semi-counter to Ratchet Bomb, and can charge up your ascension fairly quickly.

Could be better than See Beyond.  Don't like revealing my draws in a deck with Spell Pierce and Mana Leak, but it is probably better than See Beyond.

Twitch says "draw a card" on it, which can't be ignored.  It is the closest thing to Into the Roil 5-8, though it does things differently.  (It can tap manlands, and it is arguably superior as an answer to Titans.  It also taps Land or artifacts, which means your copied Twitches always draw you a card, which is a problem Into the Roil sometimes has, against one potential target.  It also "Answers" manlands for that turn, which is sometimes all you need to try and draw into more card drawing, or removal, or charge up the ascension while netting even.

See Beyond only nets you up one card, at sorcery speed, and does terrible things like shuffle your deck, or cause you to misplay by shuffling your out back into your deck.  It does shuffle land back into your deck, so you can draw it again, and gives you two shots at PA rather than the one Twitch has, but Twitch does something, while See Beyond does nothing.

This is a card that really, really, seems worth considering.  It's instant speed card draw, which is awesome with countermagic, and it's a stall card on top of all the advantages it has otherwise.

Anything that says "Draw a card" should be considered for this type of deck, and this option costs a grand total of "U."  It kills various walls, spawn tokens (but they'll sac so you don't get to draw), prevents a point of damage here or there on Bloodghasts, Kiln Fiends, Teetering Peaks.  These options are probably most relevant for Kiln Fiend, since killing a wall (instead of letting it chump), drawing a card (to keep fueling the KF), and only costing one mana (to let you play even more spells to pump the KF).

This seems like it has the most upside with the KF plan against ramp, control, etc, to kill off their 0/4 and 0/1 blockers, or to prevent their Cobras from trading with the KF.
This is pretty good Kiln Fiend tech, but probably only sees play there, despite it being a 0-card answer to Overgrown Battlement (a hard card to deal with via red spells).

Strange:

Aggro decks are getting good use out of this against decks that try to stabilize with a Titan of some flavor.  PA is not exactly an aggro deck, and we don't have Viscera Seers, or Bazaar Traders/Flings, to make sure the bad guy stays off our opponents side of the board.  If we were more burn-oriented, this could be a pretty reasonable finisher, against Titan control. Not an awesome answer to Frost Titan unfortunately....

Multifunction removal seems like it should have some utility in a deck like this.  Kills Eye of Ugun, Valakut, Mimic Vat, Ratchet Bomb, Sword of Body and Mind, Emeria, WW manlands, etc.  It's probably too slow, and works poorly when they go "summon titan, sac KHE, you dead yet?"  But it seems like it should work okay in matches that drag out, and center around specific functional lands, or counter artifacts (like the ones listed)

4-mana semi-answer to titans.  At 6 mana to clone a frost titan (and just get tapped down by that frost titan), or 8 mana to copy it and target (to take the initiative) it's probably better to just play Frost Titan, since that actually solves the problem, and doesn't require your opponent to have resolved a titan of their own.  If you are Ascended, it gives you control over a singular titan.  This seems like a profoundly fun card, and it is a Sorcery, so it combos with the Ascension better than, say, Clone, but getting to 9 mana in a deck that maxes out at 4 otherwise is probably not going to happen, despite the hilarity of cloning Acidic Slimes, or other titans 5 times (10?) times.

Speaking of mini-ascensions, this one is pretty multi-functional.  It lets you copy your own spells, but it also lets you copy your opponents.  It works to counter most counterspells (not Flashfreeze), copy card draw they cast, or ramp spells.
It seems like most of the time, this could/should only be useful on your own spells.  The best draw any other deck is playing is Preordain or Explore.  It doesn't deal with Jace very well at all, so if you are trying to counter counterspells, and also deal with Jace, Negate is probably a superior choice.
Reverberate doesn't charge up PA very well, unless there are Reverberates in your graveyard when you cast it. (By the time it copies a spell, it has already been cast)    I'm pretty sure it works well with rebound spells.
Lastly, it's pretty heavy Red, so it's hard to copy burn spells, but if you are ascended, a bolt + Reverb does 12 damage.  Just as much damage as 2 bolts...

A better "Swerve" in all ways.  And I did like me some Swerve, but Blightning is no longer around to be million-for-oned.  Counters counterspells (Like Negate), doesn't counter Planeswalkers (unlike Negate), and often doesn't save your ascension (unlike negate) from targetted removal, since they often don't have an enchantment to blow up when they kill your Ascension with a disenchant effect, or better yet ratchet bomb.
Want to buy Blightning back in standard?
Seems mostly worse than either Reverberate or Negate at this time, for this deck.  (Doesn't counter or mirror their card draw, etc)

A pretty silly card.  Would be pretty amazingly playable if they didn't untap, which probably means it's pretty non-playable as-is.  If PA was more of a combo deck than it is (ability to "go off" in one turn), this could be a sort of Silence, or Fog, or something else.

Works on all perminant types (ala Boomerang).  Competitor with Twitch for the backup Into the Roil slots.  Works against land, both manlands, Valakuts, and so on.  But without the draw on Into the Roil, Twitch is probably better?

Kills Ratchet Bomb, Mimic Vat, Argentum Armor, Sword of Body and Mind, Adventuring Gear, Wurmcoil Engine(?), Lux Cannon(?), Steel Overseer(?), Myrs(??).It is cheaper, and an instant compared to Demolish, but Demolish just seems like a superior utility card, since it also deals with Emeria, Eye of Ugun, Valakut, 3-colorscrew, Worldwake Manlands, and so on.  Shatter may be better against control, because you do it end of turn, and more easily play around Mana Leak/Spell Pierce, but that's the balance between power and speed?

I'm pretty sure you don't have to sac the x land again, because the costs for the spell are already paid when you copy it.  Could be a more legitimate wincon than Kiln Fiend late.  Good vs. Mana Leak, bad vs. Negate. 
Conclusion:
Staggershock, Mindbreak Trap, Twitch, Negate, and Treasure Hunt are the frontrunners.  (Some even threatening to replace main-deck cards)
Demolish, Twisted Image(With Kiln Fiend), Arc Trail (vs Pyroclasm, Staggershock)

Staggershock should be pretty awesome against aggro, but do you take out Mana Leak, Into the Roil, or See Beyond?  Or replace Pyroclasm main-deck  I like that (because it is less dead), but Pyroclasm often kills 2 guys RIGHT NOW, or 3 guys, or all the plant tokens, Elspeth tokens, and so on.  (But Staggershock could just kill Elspeth, or Jace, or go to the dome)

Mindbreak Trap seems better than the Negates I currently have in the sideboard.
Demolish seems better than the Spreading Seas.
Twitch competes with Staggershock (What am i going to do, take out ITR to put Twitch in?  Take out See Beyond?  That's probably reasonable..)