For a short overnight flight from JFK-LHR on a 777 ? My vote is no.

Save the miles for LHR T5 -JFK for the full BA F experience. For a first First experience, its not the best. Most pax will want to sleep and the meal service is rushed to turn down the cabin lights as quickly as possible.

CW let you use the JFK T7 FastTrack queue, same as First. You get pre-flight dining in the CW lounge. Saves you from eating on the flight since it is a sleeper service.
You get you used the CCR in JFK and pre-flight dining; only to eat again when you board. No nice arrivals lounge in LGW or CCR breakfast room for First pax.