You have two decent options to get to SFO. LHR-LAX-SFO or LHR-JFK-SFO. You should look for an LHR-JFK segment on the 77W. The JFK-SFO route will be on the A321T, which has lay flat seats in J.
I've used AA Vacations a couple of times now to save a bunch of money in J. Flying LAX-LHR-PRG in a few months for less than $2400 pp.