That connection is theoretically doable, but bear in mind that AA requires international departure passengers to be at the gate no later than T-30 (T-10 is simply when the cabin door is closed). If the onward flight is overbooked and still oversold at T-30, OP will be bumped at 7:14 PM. His connection is at risk at that point. There is a later BA service, arriving at LHR at 4:05 PM, thus 1:40 later and AA will rebook OP if he misconnects. But, that is space available and if OP is in Y, this will be a lousy middle seat for a 10-1/2 hour flight.
Given that OP has an inflexible schedule, there really isn't much to be done other than perhaps travel with a small carry-on which he won't have to gate check and thus not have to wait around for valet luggage.
If OP could possibly depart TUS 20 minutes earlier, he could have a 1:34 connection at PHX and be in LHR at roughly the same time (BA nonstop xPHX). I would make those arrangements now as the rebooking situation may be grim on the day of travel and OP is already willing to spend $250 for 5* service.
This all comes down to risk tolerance. What are the consequences of an earlier departure from TUS or a later (perhaps next day) arrival into LON?
Last edited by Often1; Jan 9, 2018 at 8:42 am