Gosh, pretty long on the A times. Have you tried just getting him down for a nap at 1hr?
I wonder if you are able to bring a bassinet into the family room where you are likely to spend most of the nap time (even if you are a bit in and out)? It is safer to have LO sleep in the same room you are in and I have read before that LO knows if you are there even if they are asleep, I read something about the breathing and heart rate being in tune with Mummy's, no idea if there is any factual evidence for this though. I did experience a similar sort of thing with my DS, he was a few months older though but we were struggling with short naps and one of the things I did in the end was stay in the room with him (I actually left him to go to sleep as he self settled easily at that time but not with me in the room, so I left the room for a few mins then went back in and lay on a bed by his baby hammock), it marked the end of our short naps and we both slept 2hrs. I will never know if it was coincidence of course.
Could you try a bassinet in the family room? You could shush/pat or rock slightly with a firm hand over the transition as needed perhaps?