K.L.
Personally, I would not put him in pullups. In my experience those things sabotage kids and make them regress, but that's just me. Also, to a 4 year old mind that's just a green light to not even bother trying.
Since you are fortunate enough to be noticing a pattern here can you start waking him up at 6:45a and have him sit on the potty and empty his bladder and then have him go back to sleep? The reason I suggest this is because perhaps it will help him to start waking up on his own. Maybe try it for a week and see what happens?
My 4 year old occasionally pees in her sleep although not very often anymore and what we do is double sheet her bed with a waterproof pad in between that way all we have to do is strip the top sheet and pad and get her into some clean jammies and she can go right back to sleep.