I don't like the term fiddly because to me it indicates you never get any consistent results. Most reviews when they say fiddly are just talking about how much has to be tracked which in my view isn't fiddly.
It can't be fiddly. AA doesn't have a fiddle.
fiddly
adjective -dlier, -dliest
1. small and awkward to do or handle
Nowhere does that definition imply inconsistency. It's just a matter of whether Sentinels has a bunch of tiny, awkward moving parts. Which is an interesting question.
On a surface level, Sentinels of the Multiverse is a lot less fiddly than games with a lot of small physical components, like Mage Knight, or Arkham Horror. However, the interactions between each individual card on the table can create situations that are sometimes much more annoying to parse than either of those games. The question then becomes whether the amount of fiddiness is worth it for the game inside.
I certainly don't blame people who don't like Sentinels for being fiddly, though I might question them if they then said they liked Arkham Horror, because I think that game is the King Fiddler. Personally, as someone who can enjoy Mage Knight single player, I can get past the bookkeeping issues in Sentinels. Most of the time. Sometimes, if I'm using a randomizer and roll someone like Kaargra, the Chairman, or the V5, I might re-roll just because I don't want to deal with all of their nonsense.
I don't get Sentinels being awkward, that's why I don't say it is fiddly, complex yes, randomness interrupting that and making it even more complex, yes. Awkward, I don't see it.
They are just different ways of saying that the mechanics disconnect you from the theme of the game.
I have yet to see this happen with my own games.
Have you tried playing WGL, PW Fanatic, and Argent Adept together? Trust me, the theme gets lost in the complexity of "Who hasn't used a power yet?" Complexity kills the theme. And is awkward, making it fiddly.
I don't have any promos right now, so of course I haven't played that. That does sound like an edge case, however, and not so much what one can expect from the game as a general rule.
Go to Google, type "SotM Promos", and go to the Board Game Geek entry. You do not need to have the promos, just print them B&W and Glue them to playing cards until you can print them better.
I printed them in colour off the Library's printer, glued back to back, and had them laminated at an office supply store. The colour is dark, but they are much better than nothing. Ran me about $22.00 for everything.
Given the absurd costs for Canadians (I pay 2x what a US customer does for the same product from GtG, after Customs, and no lie there is a FAQ entry here for this), I won't be pre-ordering anything, and thus will never get a true promo card. I'll be waiting for Villains to hit the shelf at my local game store. This is the only way I'll get promos.
Not even eBay is an option. One $2.50 promo card turns into $45.00 after shipping, and add $20.00 more for Customs.
Yeah, I've been through googling everywhere for them and such. I'm going to order printed promos from PrinterStudio next month. Or if not PrinterStudio, there's the other option whose name I've forgotten.
I do not have a printer, so I can't exactly just print them whenever I want. My alternative was going to be to go to Kinko's, but PrinterStudio looks like a better option and I don't want to pay twice.
Once I have cards in hand I want to try your suggested lineup, so everyone can give everyone else extra power plays. 
Once they're done with everything for the game, a package will be made available to buy of all the promos.
True, but I am impatient and don't want to wait a year. :D
Print cheap or just scribble out on an index card.
PrinterStudio is pretty inexpensive, and the card quality (from what Silverleaf has said) is fairly good.
I have been tempted to do index cards but I haven't yet felt the need. I'm still familiarizing myself with the various heroes and villains without throwing the promos into the mix. I do want them, but I've found what appears to be a satisfactory solution for that.
It's better now, especially if you can join/organize a group buy. We have 11 people in the latest one (Halifax NS) and the average shipping cost for the VotM order is $2.73 per person. Even with just 3 people on the Tactics order, the shipping averages $6.66 each. GTG now has a Canadian shipping process that avoids customs fees, and while I am always ready to pay HST, it hasn't happened yet.
I'll agree to the complex nature of the beast, but in my groups, it's not an awkward gaming maker, just 1,001 different little thingamabobbers all going off in a sequecially ordered order. There have been times an effect that should've gone off every turn was remembered by someone 3 or 4 turns later, and we all had that realization that we forgot to do that. it happens to the best of us with gaming.thankfully we've been playing the ever-living hell outta this game, so it's been getting imensely easier for us to handle it. that's all it really takes, a few run throughs to get the ordering fiasco right, then working on the smaller details.
We find it helpful to mark effects that can trigger without the deck area the card is in being involved.
What I mean is cards like Shielding Wind, Tempest doesn't have to be involved. We don't mark Infiltrate and Obfuscate or Hairtrigger Reflexes because those involve their character acting, and if you can't track your hero's effects you learn pretty quick to go for less complex heroes.
Mostly we end up marking Environment cards. 4-5 marked cards, we use one for damage modifiers and another color for reactions, tend to be easy to scan, and cards that don't act out of turn like that are usually pretty easy to keep track of.
Outside of playtesting we rarely have errors anymore, new decks take awhile to learn.