Amazing itinerary
The LAX-LHR-LAX route has my sympathy, same as DFW-FRA-DFW !
You're a regular AA customer with 1.9 MM, so you have plenty experience to figure out the best pricings and booking classes I guess.
These booking class stuff always drives me crazy because aa.com doesnt show it... How do you handle this ?

Do you plan full EQM/EQP classes of low budget ?
I made several MR's on the mentioned routes and also on the LAX-NRT-LAX while the promotion period

Hard days but with the bonus it was worth it!
Trip report appreciated, have fun