There have been a few threads about TAM having no capacity controls on award tickets. If those posts were correct (and the policy still stands), why don'y you book 7 J tickets on TAM?
I have never been on a full 995 MIA-GRU. Most of the time less than half of J is taken. I can't think of anything in Brazil that would make November any different.
As for JFK, that flight is normally much more crowded, but Delta is adding service so that might take a little of AA's traffic.
I think it is worth checking into TAM.