If you can get an evening flight the day before you’d normally travel without extra costs such as taking more time off work, there are evening flights to JFK or BOS, you could stay there and then take a direct AA flight to SFO the next morning. On the return you could do LAX-ORD, then stay near ORD and then get the daytime AA flight to LHR the next morning.
Play around with the AA website remembering to select ‘all carriers’ as the airline option.