Any chance at all you could book JFK-LAS in F? (You'll have to telephone and ask for a quote for a multi-cabin booking.) Of course that segment would net you 210 TP if booked under the AA code and you'll be laughing. (You will need to be specific that you want the AA code, not the BA code, but it shouldn't affect the pricing.)

No idea how BA would price it though ... can't hurt to ask?! Other concern is that making it complicated may affect your ability to UuA, I can't say.

Alternatively maybe you can go LHR-LAS//ORD-LHR as an open jaw BA itinerary in WT+ (or UuA to CW), and then nest a TP run to SJU, perhaps one way only, as a separate itinerary, and then economy back to ORD, all on AA. (Or indeed substitute JFK for ORD.)

AA will protect you if you misconnect your LAS-...-SJU segment, even across bookings.

Edit: Made it unnecessarily complicated. You could also do, like you suggest, LHR-JFK//LAS-LHR on BA and JFK-LAS in F on AA. But that JFK-LAS flight will not be cheap at all.