I am doing the same in November - AA JFK - LHR and then BA LHR - SOF all J class.
My worry is that I booked the AA trip on AA.com and the BA trip on BA.com - will they be able to check my bags through? Also, is there any danger of being accused of "nesting" when they realise I book lots of journeys that overlap?
I have a 2 hour stop. I had though that was more than enough until I read this thread. If they won't check my bags through I am well and truly stuffed!!