I've got a small 10"x10" pillow I kept from an Air China international flight, put a cover on it, and been using it for years to tuck behind the small of my back.
I just looked up FLL to PHX, and there are no direct flights except for Spirit Airline on a n A320 so are you taking a connection? There seem to be coach 1) AA flights on A321 so it means you need to be flexible on your flight schedule, and 2) Delta and United flights running 757 and A321; obvious a few 737's that you're trying to avoid. If status/miles isn't incredibly important to you, try Delta and United. If status/miles is incredibly important to you, you'll need to rearrange your flight schedule accordingly to fit the planes you want (or just cough up the money and she doesn't fly coach).