You need 1 sq foot of ventilation per bird, reguardless of how often you clean the coop. I highly recommend you go uncover your vents and stop worrying about the cold, they'll be find.:]
Flat panel heaters operate like brooder plates, they don't heat the air, but they will heat up the bird if their touching it. Not going to work with 23 birds.
There's no way to heat up a properly ventilated coop. Save your back and stop hauling heavy things. They WILL be fine.