I mentioned it last year, and finally booked it for this year, there's a SOF-LHR-JFK-LAX-SFO and return AA fare in F for TATL and TCON for 2.7k£ (just above 2.5 £/TP with the exchange rate). Both TATLs can be on BA with AA codeshares (I have 747s both ways).
Depending on the flights, bookwithmatrix actually works on aa.com (first time for me, but not with all combinations). The fare (INX9C8S4) has a 90-advance purchase and Saturday rule. It might be possible to tweak it a little more but I don't think so, I've tried adding a West Coast element or a HEL shuffle but to no avail. If I remember my previous post correctly, there was a slightly cheaper version from ARN or OSL.