Maybe it is because I tend to qualify by EQP rather than EQM, but in your case I would be very tempted to fly economy to the USA and Y+ back to England. Using ba.com to book, in order to upgrade only the one direction.

As a result of the JV, you'll earn the same base mileage to an AA account. And on the return get a seat better suited for sleeping along with 1.5EQP per base mile. This strategy also avoids the UK APD tax hike for "improved" cabin seating.

Happy wandering

Fred