Having checked, on most days in December there is abundant availability in WTP on the BA174 (18:55-06:55) out of JFK connecting on to BA143 (11:45-01:25) giving you a 4 hour 50 minute layover, similar to your original booking.

I would ring back quoting section 9a3 of the T&C's of carriage that I mentioned up thread and ask to be moved to those flights. If the agent is unwilling to help escalate to a supervisor. Sadly the US call centre seems to have some rather poor staff working for it amongst some of the very good ones.