I think going through Buenos Aires twice is the only way to get from Mendoza to El Calafete. I would just be connecting first time and then visiting for a week or so the second time before heading back to the U.S. The stopover would be MIA for a few days. Yes, you are right it's EZE not AEP but now I realize there is hardly any availability through MIA so that stopover might not work out.

I used a mileage calculator to come up with the Avios miles needed. To book I figure I need to call British Airways to book LAN.

Thanks for the tip on using AA within So. America. I'll have to figure out how to get from MDZ to FTE on one ticket since they seem to go through different airports. Anyway, it's still fewer miles than how I was structuring it.

This couldn't be more complicated! Too bad none of the airlines can book on partners easily!