I'd book the AA flight because AA is most likely to be sympathetic if there is an inbound delay, as AA and BA are both OneWorld, and you'll get lounge access due to connecting from an international business flight.
With global entry, I'd expect you to be curbside in JFK around 25 minutes after landing (so effectively, you'll be out before your bags), and you would then need another 20 min between terminals, plus another 40 min to drop off economy bags and get through security. So around 1h 25 + time to get to the gate and board is reasonable, albeit minimum connect time is officially 2h all-in. It means you can be up to 2h late on the inbound and still make the connection.
Not sure if you either can or should (given the change fee + additional points cost) book AMM-LHR-JFK-RIC on one ticket, but that may also be worth considering.