Part of the problem is going to be availability. If your stopover is more than 24 hours, you will need A inventory on the JFK-LHR nonstop; it’s treated like a stand-alone flight. AA is very stingy with this. If your time in New York is less than 24 hours, then your trip can use married segments, which have much broader A class availability for that JFK-LHR flight when sold as part of a BDA-LHR journey.