I had this exact problem when Nina was around 4 months old, which lasted for about 6 weeks (sorry!). We had a very similar bedtime routine to what you do. I just kept trying with putting her to bed awake, until one night it worked. She would whinge first, not cry, but then went back to sleep.
It sounds like once awake, he can't put himself back to sleep. The only thing I can suggest is keep trying with it. Does he have a comforter - dummy, teddy or something? Or how about a top up with EBM, while he's still in his cot? I'll keep thinking of what we tried at the time and come back to you.