Re: replacing inner cover with a fabric or plastic
Burlap works great. It also offers a some hive ventilation (not too much). Indeed the original idea was that you could peel back one side and not disturb the entire colony.
One benefit, is that if you use fabric for a season, it gets all filled with propolis and bee smells. Its a fantastic addition to your swarm traps to get all the right scents into the box. Cycle them out in the spring to get the fresh scent in the swarm traps and new cloth on the hive when they can tolerate a bit more air movement in the hive. By winter, they should have less air flow, but still offer a bit of absorbency to reduce condensation dripping into the hive.