Unless something strange happened last year, you would have cleared immigration, claimed your bag and cleared customs at Atlanta although you would then have given the bag straight back to the carrier for the domestic flight. This happens even if the bag is through-tagged to your final destination and you have already been issued with a boarding pass for the domestic leg.
This year Virgin should be able to through-tag your bag LHR-MIA-RSW even though the flight to Fort Myers is on AA. They are not obliged to if the AA ticket is a separate one but in my experience major airlines are usually very good about this. If your bag has been through-tagged you should be able to give it to AA immediately after you have cleared customs at MIA, before you have exited into the landside area.
I doubt that VS will be able to give you an AA boarding pass and you will have to get that at MIA. I don't know if you will be able to get an AA boarding pass at the same place as they take the bags; you may have to go upstairs to the check in area. (If you are feeling cheeky and you have time at LHR after you've checked in with VS, you could pop over to AA who are in the next check-in area - IIRC, VS uses Zone A and AA uses Zone B - and see if they will issue you with a boarding pass there. Be prepared for a no, though.)
One advantage that you do have at MIA is that there is only one horseshoe-shaped terminal building, although there are a number of concourses that radiate from it. It looks like VS arrives at Concourse E and the Fort Myers flights depart from Concourse D so at least you don't have to walk the entire length of the terminal building to get to your connecting flight. The concourses are still pretty long fingers, though.
If you are doing the same itinerary in reverse on your return, AA should be able to through-tag your bag to LHR and automatically transfer it to VS at MIA so you would only need to collect your boarding pass from VS and go to the gate. VS will almost certainly want to see your bag tag receipt so have that handy.