I hope that pic was taken at night...a cham sitting with eyes closed during the day is in trouble!
I've kept melleri free ranged and know it can be done. It can be tough to thoroughly cham-proof a room. One concern I would have is exposure to UV light. Unless he has access to a lamp such as a ReptiSun 5.0 or gets outside in true sunlight a lot, he may develop MBD. Curious, why are you feeding dead prey? Live prey is much more nutritious. You can set up a feeding bin for him. Get a plastic critter keeper and put it somewhere he can reach it easily such as near his basking spot. Each day you can put live feeders in it with gutload. He can hunt from the rim.