I would book the itinerary you have suggested. It works for your schedule; you're getting good value by using AA miles (the same itinerary booked on BA with BA miles would cost you 330,000 miles); you're avoiding the UK air passenger duty by only connecting through LHR; you'll have access to You First if needed; you'll be able to preselect your seats for the TATL legs on BA in first; and the T5 "experience" when it's working is quite nice, especially with access to the Concorde Room and the First lounge during your layovers.

I would pay the YQ surcharge and book it.