Thanks all for the replies. The exact travel date is 9th Aug, which happens to be a Thursday. I'd estimate that after landing, customs and collecting bags we'll be out of the airport by 18.30.
I'll keep my eye out for SFO award seats to see if any pop up. We live ~50 miles north west of London so LGW is a pain to get to.
If we end up spending $100 on an Uber into San Fran then I guess that's the way the cookie crumbles.