Ok, so it sounds like you are doing all you can to get him to sleep, and he's just not co-operating - right??
I wonder if the naps that he struggles with could be in a sling, just to get more sleep into him. Would that be something to try?
I remember my little guy being very unsettled in the early mornings too, for a while. he grew out of it but this is the time that I handed over to DH as I was just too tired to manage after feeding in the night too. Can you get any help?
There is a balance to strike, for both of you. Yes an OT baby is not nice to deal with, but staying home all the time so that he can get some sleep is not good for you either. When you are up to it, taking him out and letting him sleep in the buggy for some of those day naps is not going to do him major harm (may even catch him up?) but may be good for your mental health.
Take care of yourself too (the old oxygen mask thing!).