What is the fat % of the dry food and wet food? Are you using low fat options? Do you feed any insects, if so which ones? Wet food is generally a lot higher in fat, is there a reason why the vet would suggest it? For more protein (and fibre) you could feed low fat insects like crickets and dubia roaches.
I read before that scattering the food around the enclosure, so they have to find the food and work a bit to get it can help them become more active. With the wheel, can it support his weight? You might have to get a bigger one as the CSBW i think is 12" in diameter. He probably could do with a 13 or 14" one. I've been looking at the hedgehog precision one as that's 13" or so I think and looks more reinforced on the wheel rim. Also have you seen him try to run on it? Perhaps it's bowing under him and scraping the floor when he tries to run? My boy gained a lot in weight earlier is year (almost doubled in size but he was tiny before so wasn't necessarily a bad thing but he could do with dropping a little). Anyways he stopped wheeling as much as he used to and when I changed the tilt on his wheel aimed more forward I think it may be have bowed a little when he tried to run, hence he stopped using it as much. Recently we tilted it back so angled a little backwards and he's back to running marathons on it.
The itching and scratching may be due to excessive skin, if he has any rolls under his arms etc. does he skin look red?
If you turn all the lights off in the room, will he still not wake up and start exploring? Again you could try scattering food around your floor, turn the lights off and see if he'll go walking around to eat, not leaving him unattended of course.
Hoping he loses some weight soon!