My input was in response to you listing out your 10 cross-class abilities and questioning the need for Aero to be on there. There is an argument for Stone being there due to the MEVA down effect. I cannot find a proper reason for Aero being there though. At -13 / tick for a maximum of 10 ticks you're looking at 130 damage in addition to Aero's initial damage. This may not even add up to 200, or the average damage of a single basic Thunder. There is no known special benefit to having a DoT present in this case (for instance, it does not surpress Ifrit's high Regen rate).
Regarding Invigorate, I agree that it's just easy to use and I use it as well. I feel like for optimization you should drop Aero and replace it with Quelling Strike. The argument that "we do fine without it" may be true, but is kind of not relevant in a min/max discussion right? It's true you're fine either way, but it's also true that you would be more efficient (albeit not by much) with Quelling.
Regarding Stone. The argument that it's useful for the -29 MEVA is a bit more dicey. I still feel it's not useful simply because if you look at the average duration of the MEVA down, it is definitely not the full 30+ seconds you see on many other debuffs. It may only last 10-15 seconds maximum and it's pretty consistent. This means it'll probably only be active (if it even lands) on your next 2 nukes. Ifrit is essentially an exercise in dodge > Thunder > Thundara > dodge > etc.. I question how much time you actually have to throw in another nuke (stone) w/o compromising safety, though it's hard to back this up with something as simple as a paper formula.
Finally, regarding the overall concept and use for a move like Quelling Strike. We must remember that a THM's damage is limited by 3 factors - resist rates, MP pool and regen rate, and enmity. One of these 3 things is going to limit your output. For Ifrit with a half-way decent MACC set, the limiting factor is by far going to be enmity. This means that to become more "efficient" from a DPS perspective, increasing damage or MACC really doesn't improve overall DPS that much because you'll be capped by enmity anyways (you just may need more nukes to get there). The only way to reliably increase the DPS would be to increase the enmity generation of the tank or decrease the enmity generation of the THM. Quelling Strike does this, and although we all agree it's "lackluster", but will certainly provide you more benefit than -29 MEVA for 10-15 seconds after a Stone cast.
EDIT:
Thinking more about this and Aero. There may be an additional benefit in that that +130 damage you get from the Aero DoT effect is not counted towards your enmity. So it's essentially 130 "free damage" (which is basically the same as Quelling). So from this point of view I can actually concede that Aero does have a benefit on DPS (it just won't be seen on a parser). So I guess the question to have Quelling on your bar comes down to Stone or even Invig versus Quelling. I'd still argue not to use Stone but at least I can give a valid reason to use Aero for increasing DPS.