Jacob-
Thanks for the advice. Yes, I'm flying in on 981 and out on 5736 (UX). It seems that UA5736 normally leaves from C22 so I might have some breathing room there. I definitely should check the hours at the BA Lounge...my PP app says 7AM-2PM for PP members. Unfortunately, it's at the B Concourse anyways which might make things difficult and ESTA immigration clearance isn't all that predictable....(45 minutes at SFO. Then again I arrived on KE just after an OZ flight from ICN)
I guess if I travel without checked luggage, I might be able to squeeze it in if I move quickly. Worst case, I'll have to go to Spa Castle.