I had a look at F fares for late April. Arn-Lhr-Jfk-Lax-Sjc were pricing at about 2850 GBP return midweek, which would bring the trip to 1000TPs at 2.85 per TP. Not ideal but also not too expensive compared to recent trips I tried to price. SFO also worked on some dates.
My only question is can you use the CCR if flying first on BA F but on an AA codeshare?