Looking at availability in both Club and First that's been posted, it's very tight on BA operated flights. The code share flights operated by American are the ones with more room.

Given it's a popular time of the week for business travellers getting to NYC ready for work on Monday morning, and therefore all the flights will have a lot of other passengers with status, put thoughts of an upgrade out of your mind.

Besides, WT+ is perfectly fine for a day flight to JFK. This also gives you a chance to enjoy T5 and not head straight to a lounge. I'd recommend Plane Food for a nice lunch to while away the time before your flight.