If you can't find business seat for MIA-EZE-MIA, check LAN Argentina (4M) on Qantas.
You can fly MIA-DCA-MIA in economy but if you use AA miles for one award, it will cost you the same (50K) but you will save 7.5k Avios points.
Another option, from MIA-EZE it will cost you 50k but if you want to stop in LIM for few days, it will cost you 45k