I would be tempted to find a daytime flight if one exists - say BOS-LHR, leaving Boston in the morning and arriving LHR in the evening. Overnight at one of the airport hotels and then LHR-IST the next day.

If I were flying to Europe with our 1 1/2 year old, that's what I would do. He doesn't nap that well on planes or in his carseat in general, so I wouldn't want to do the one of the red-eyes, and would try to keep as normal a schedule as possible. Just my 2 cents.

Definitely worth the extra seat, IMO.