Honestly, MIA is not that bad compared to other US ports.
I was there a couple of weeks ago, and it took 50 minutes, a rapidly moving line and cheerful agent when I reached a desk. I was, however, first off the flight.
The previous time, a few months earlier (before the Budget issues) it was empty and I sailed through.
Be prepared for a lengthy 10 minute *march* through the terminal to get to immi – sensible shoes are advisable – and a further *march* to the new Rental Car Center.
I would suggest Tampa from Gatwick, if you can brave Club instead of First; it’s only a 3h30 drive to FLL from there. Dreamy immigration and a very well laid out terminal.
I did Philly late last year and that took around 30 mins, which was acceptable, but again that was before the cutbacks.