If you arrive in D after 12:00 noon and are on ITI - and GUA to LHR is certainly ITI - go to the ITI facility, takes maybe 1/2 the time, your luggage goes through without customs and in the ITI facility is a combo INS/Customs agent, and a private TSA facility after which you exit, still in the terminal and already through security.

If you arrive at E and they try to stuff you into the regular lines, do not fret, go to the back of the entry room where the AA desk is, leave that room from the door on the right (your right while looking at the courtesy desk, thus with INS agents booths at your back), go over the people mover conveyor belt , turn right at the end and you are at the ITI entrance.

You are essentially walking back into the D arrival gates but get to the ITI entrance before actual gates - or if you are uneasy just ask the AAgents at the courtesy desk to point you to the ITI pathway.

ITI in MIA is the only way I would risk an international arrival connection in MIA under 3 hours. I connect from MGA every month or so and the early flight allows only 90 minutes and I have missed my onward flight too often to bother trying anymore.

The bad news is you invariably arrive at D/E and your LHR flight will be from A. Or the other way around.

NB: AA will of course give you the GUA-MIA and MIA-LHR baording passes in GUA.