I apologise in advance if this has been posted in the wrong forum.

I have an upcoming avios booking LHR-IAH in F on BA and want to connect same day to MIA on AA which will be a separate booking (not yet booked).

I understand that I will need to clear immigration and customs, collect luggage and change terminals from D/E to A.

My question is how long does the subway take from terminals D/E to A and ultimately how much time would you allow between the 2 flights? Additionally, would it be easier to fly UA as I see that would depart from terminal E? Finally, I assume AA would be favourable for the lounge access?

Any advice would be much appreciated.