What I dont understand is why your taking it out and only allowing him to use it for a couple of hours.
At 1 years old, they like using their wheel more, when he was younger it wont have mattered so much. But at 1 years old they get MORE active and like to use their wheel more.
Also at 1 years old they can change when they feel waking up and some wake up later than they used to.
I understand you wanting to give him that play pen space and time, and thats honestly great, but if he knows he wont get his wheel when he goes back then he will want to make the most of it.
I cant see any benefit of not leaving the wheel in for him to use whenever he wants throughout the night. Especially if he seems to like his wheel so much.