Flightmemeory tells me I've flown JFK-LHR a cheery 61 times. sigh.
To maximise the experience in JBA F, I would choose:
LHR-EWR in F on the 787-900 - only 8 seats in the cabin and it's BA's best seat in the fleet. Careful as depending on your dates the 789 may or may not be on the route.
JFK-LHR on the AA operated AA100 (BA1511)- arrive nice and early at JFK for the AA First Dining Room. It's more exclusive than the BA JFK CCR and has a much better food and wine offering - £120/bt Krug NV champagne, £40/50 bottles of red and white (vs £30/bt Laurent Perrier NV and £8 red and white in the JFK CCR). have a leisurely dinner, cocktails, get on the plane and go straight to sleep. Land LHR at 6.20am before Terminal 3 gets too busy and you can be in Central london at 8am with a good night's sleep under your belt and the full day ahead of you.