May I ask if they have a room to themselves why it's an issue if he gets out?
If it's glider proofed and the door is secure I think I would just hang a pouch outside of the cage so he has a place to curl up and sleep.
I say this because my room is glider proofed and it's the space they play in and there have been several occassions where they will sleep the day away in there.
I hold my curtains back with a curtain tie and where it's tied back the curtains make that layered dip thing...my 5 just crawl up and snuggle in the layered dip and sleep the day away. I've even put a sweatshirt in the middle of my bed and they've all curled up inside and slept of that.
Zoey learned that she could get into my dresser from the back so I've caught her sleeping in my sweater drawer on 2 occassions.
Of course my room is completely secure for them and I have no one around during the day to leave a door open so I know they are safe. If the room you have made for them is the same way....secure and no accidental door ajar issues can come up I don't see why they can't have free reign of the room.