A couple of tips:

1. Search for one, two, or three seats on your desired flights. It's possible that there are some lower-priced seats (for either miles or cash) available; you might be able to snag one, two, or three cheaper seats, and just purchase the remaining seat(s) at the higher price

2. If FLL is an acceptable alternative airport for you -- in either direction -- check mileage and cash rates for that airport. But if you fly AA, you would have to connect somewhere: AA does not offer nonstops between FLL and PHX in either direction.