I can not judge IBs J or Y Class, but their F Class is very good since they introduced their flat seats a few years ago. It is not a full bed, but reclines 180º, like old SQ or LH. Service is superb, at least for Spanish speakers.

In addition I think you would be nuts to fly through LHR and MIA, and add 12 hours or so to your trip.

In any case, I would make detours to avoid AA abd UA