I would try AC. A quick check shows scattered availability for 2 C seats LHR-YYZ-SFO and return, e.g. out 21/9 return 27/9. There may be other dates and other routes from European airports but I didn't check those (or your connections from MAN).

If you're using ANA it won't find these by default if you just ask it to look for LHR-SFO, so you can either search sector by sector or specify your transit city (YYZ, YUL, YVR).

West coast is always tricky though so best of luck.