That's what I do with my Redfoots outside in summer and inside all winter with no artificial UVA/UVB.I think your closed chamber is to open. If I misted my closed chambers for 30 second once a day, they would literally be sopping wet in a few days. I add no moisture to them. The only moisture added is what the tortoises themselves track in and out of the water bowls. Each of mine has vent slits in all along the back and sides, and the front doors have 1/4-1/8 inch gap too. Room humidity is usually around 30-40%.
We have warm spells in the 70s and sometimes 80s all winter long here, so sunning is never an issue for me. With that, the RepCal, and Mazuri, I'll never see a hint of MBD. I'm reminded of Kristina. She was a moderator here on TFO years ago. She had a large tortoise collection with many species. She lived in Cadillac MI, and her tortoises all lived outside in the warm summer months. She brought them all in for winter every year for 6-7 months, and never used a single UV bulb of any kind. She had no problems doing this year after year.