I for one would recommend checking the AA status/mileage run forum.
With the enhanced relationship with AA earning top tier bonus miles when flying on AA marketed and operated flights, an AA premium economy flight is for me the way to go.
I would do something like this:
XXX (anywhere in Europe) - LHR
LHR - US Westcoast in premium economy, ideally SEA or LAX.
Then some kind of destination in Mexico or the Midwest that you can connect through via ORD or DFW.
Maybe something like this: https://www.google.ch/travel/flights...r=EUR&hl=en-US
On the return you do the same.
This should yield in total anywhere between 134 to 140 Qpoints and the example costs app. 1030 EUR in premium economy.
Mileagewise: AA H class (US domesstic and the feeder into LHR) earns 100%, P class earns 125%.
This should earn you roughly 16'000 to 18'000 Qmiles + whatever your top tier bonus is.