If miles are your priority then I would say your first option is the best. If convenience is your priority then go with option 2.

I have travelled JFK-EXE-JFK on a few occasions. About half the time the metal is a 777, the other half, a 767

There are shuttle buses that travel between LGA and JFK. I have never had cause to use one so I don't know the route it takes. I would assume it takes the Grand Central Parkway to the Van Wyck Expressway and into JFK. Either one of those would be a parking lot during rush hour, but at 8.30pm you should make it to JFK quickly. I don't know if AA can give you your boarding passes for JFK-EZE in ORD. If they can then that would be a help.