The good news is that your jetlag after going West is likely to be much less bad than going East. I definitely wouldn't go out of my way to avoid sleeping in your nice F seat - if you get some sleep on the plane, then you're more likely to be able to stay awake for a fair few hours after you land, rather than collapsing in your hotel room right away and then finding yourself wide awake at midnight. You're booked on the best flight jetlag-wise, as you'll be landing just in time for the time window when light is able to delay your biological clock, which is just what you need - get as much light exposure as you can after landing (for the same reason, the timing of the earlier return flight BA284 is not great - there is a risk of you delaying your clock and ending up adjusting through a 16-hour delay rather than an 8-hour advance. Avoid light after landing if you're on that one).

I would bring some Nytol and take it at bedtime in SFO even if you're feeling absolutely shattered. Your body will experience a tug-of-war between your body clock telling you to wake up and your sleep homeostat telling you you haven't had enough sleep. I find that some Nytol helps your sleep homeostat get the upper hand for a bit longer. And if you walk past a drugstore, buy some melatonin and pop one of those at the same time - that will help your body clock readjust faster too.