JFK-LHR is, by some metrics, the busiest long haul route in the world. I wouldn't be surprised if BA makes more profit on this than half of their other American routes combined. It's very rare for there to be a cancellation due to lack of demand - other than the usual trimming down around Christmas/New Year the closest we've seen is a downgauge from a 777 to a 787 on one of the flights.

It's also not entirely surprising to see so few seat reservations 4 months in advance. As you say, BA charges for seat selection even in business class, so you can't necessarily infer the number of bookings from the number of unreserved seats.

I imagine an influencing factor for some people in deciding not to pay for a seat will be the fact that all flights on this route have the Club Suites product, and that one such seat (especially on a night flight) is much the same as any other.

That's in stark contrast to the old Club World product, where some seats are considerably better than others (such as avoiding having to step over others to access the aisle).
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The demand on this route is also much more heavily business-oriented, with the average passenger booking closer to the date of travel than on predominantly leisure-based routes. So even if you knew that 1 seat = 1 booking (as is more or less the case in First, where you get free seat selection by default) you would not see the cabin fill up until closer to departure.

Redemption seats are - by and large - more commonly booked by leisure pax who can be flexible on date & time, so together with the much higher number of daily flights on the JFK route and the aforementioned business-centric demand it makes sense that Avios redemption availability is much better than less frequent, leisure-dominated routes.

Indeed you often get decent F availability - which is rare on other routes, particularly since there is no guaranteed release of F seats as there is with the other classes of travel.

Overall I wouldn't be worried.