I would book GLA-LHR-JFK-SFO/LAX-JFK-LHR-GLA in J possibly ex EU. You could also look to replace GLA-LHR-JFK and vice versa with GLA-LCY-JFK.

Booking in J from the right origin would increase point and Avios, yield and resolve the lack of upgrade inventory issue. I woud combine this with a JFK-DCA-JFK flight booked separately with AA or another airline, depending on relative cost.

This should not cost significantly more than WTP if you pick the right origin.