Oh wow! That thing must be really hot. I've had my wool get scorched by my wood burner, or by stove element, but never by pots and pans. That tells me that your casserole dish must be really hot!
I love using my firewood glove that's made out of insulated leather, That might be the only option for your stove "door"
Nicole, several of the casserole dish lids have exploded. Hopefully mine will not! But apparently they get quite hot. Fred says the stovetop gets to one thousand degrees above the “ram’s horns” part of the flame (the bit at the top that’s sort of fountain shaped). It’s pretty crazy.
Felting it will help keep your hands safe. The holes in knitting/crochet seem to let the heat through far more easily than the solid (and thick!) surface of something felted. It'll probably make a more durable pot holder when felted, too.
I'm thinking that felting it won't help much in terms of keeping it from singeing. If the casserole dish is that hot, it'll singe the wool.