So we assume you are NOT checking any bags on either flight? Because if you are I think you can discard the whole plan right now.

If not checking/collecting bags: I think you need to allow for at least 90 minutes for getting to the gate, clearing immigration and customs and another hour to go by taxi/remise from EZE to AEP (you can probably make it in 40 minutes but you can't be sure) but then you have to also make the cutoff for airport check-in. It is not impossible that you will make it but IMO it's cutting it very close (too close for me). And any significant delay in your arrival ruins any chance.

Is there some serious disadvantage to spending the night in Buenos Aires and flying to Iguazu the following day?

One more point -- since you are arriving on AA you could consider the meet and greet by AA's Five Star service. That could certainly whisk you through arrivals but I am not sure it's worth it as the same money could pay for a hotel for one night.

Finally, I think you are wise to avoid Aerolineas entirely. But that's a whole different subject!