I have a front loading dryer that's 17 years old. I find I have to replace the felt every three to four years now. It burns up, leaving a gap in the seal between the drum and door for clothes to get trapped, or burnt felt pieces get into the dryer and stains clothes. There is no rust. My last repair, I had seen on the instructions that the paint should be in good shape on the drum. Mine is not. It has worn down to bare metal. Could that be causing the felt not to last as long? Would a coat of high-temp appliance paint help that?
The original coating was probably ceramic, which would have very low friction. Bare metal will have higher friction, which will heat up and damage the felt gasket. You could try paint (gloss, not high-temp), but I doubt that it'll last. You'll want to have the drum powder-coated or replace it.
The paint is worn down because the drum was used (a lot) with a seal. If the felt is burning due to friction my first thought would be that it is moving around. I think the main issue is the lack of high temperature sealant. I am guessing that your sealant is wearing out over time, then felt starts moving around and gets burnt up (it probably just gets finely shredded but who knows).