carlosdca

I disagree that BA CW (Business) is better than AA-F (regardless of time of the flight). The AA 777F seat is so private and comfy!

Since the OP is looking at a discounted business fare, he could upgrade to F on BA IF he is offered an upgrade for cash by BA online (res has to be done on ba.com) or ask at the airport for an upgrade for cash IF available.
Too many "IF"s involved with BA.

I have had my upgrades to F from J on AA clear at time of booking. So, if I was the OP I would call AA and check whether LHR-LAX or LHR-JFK upgrades can be confirmed. IF both are available, it is a tough call. Both have its pros and cons. I would probably pick the one that gets me to SFO the earliest