Sorry for the situation. Traveling companions are always problematical.

Others with more experience will give you good advice, but for what it's worth, I've gone from AEP to EZE and think it's about a 45 minute taxi ride. Also, EZE is very busy at that time, but as a Plat be sure to use the Biz-First check-in lines. We used First (technically wrong I think, but they were cool with it. Even found some packing tape to lock up our styro wine carrier that we insanely thought was going to be carryon) get your boarding pass, then pay your departure tax, and move right on the the AA lounge.

I think you have plenty of time, but understand your nervousness. Don't know anything about el calefate, but have you been to Iguazu Falls? Stay in Argentina, enjoy your visit, don't go home early because someone else has messed up your plans.

YMMV