BA F> UA F> VS J> DL J(varies based on config)> UA J> BA J would be my ranking. But that is not exactly what you need here.
I would do VS Upper Class with the stopover you want (not sure who you connect on) even though on connection you will not get VS benefits. If it were me I'd do VS SFO-LHR-PAR (open Jaw) LHR-SFO with a train ride back from PAR-LON.