What about AA? They are pretty strong in FLL and very strong in MIA. You could get to LHR and maybe CDG (can't remember off-hand) nonstop from MIA, which would be pretty nice, and you could also connect to anywhere in Europe from LHR. Personally, I'm a huge fan of European connections over stateside ones. Plus, you get the best lounge access on AA (first class oneworld lounges) based on the amount you fly. I'm pretty sure you'd only get business class lounges on Star or Skyteam. Plus, AA has (in my experience) the best redemption opportunities.