My totally ancedotal experience is that you will not be able to book a club class ticket from LHR-MIA until about 10 days or so before the flight. You may find one or two WT+ seats, and there are plenty of coach seats (at least for a BA Gold). Well, don't know about you, but I don't plan many vacations on 10 days notice!

The real irony...after I booked an award WT+ seat for my wife, even though I wanted (and was willing to use mile for) a club seat, she ended up in club anyway. So by not releasing sufficent award inventory, BA 'cost' themselves 25k miles...

I really can not comment on other routes, you can kind of guess from my handle where I fly...

As for AA, they will typically have 2-4 business class seats available on each LHR-MIA flight, and each flight almost always has first class availability. Now, you need to determine if this is a wise use of miles, as AA business class is below BA Club service on daytime flights, and well below BA seat/service standards on overnights...

Good luck!