1. No need to swap enclosures or put things down, a lot of people think if the snake ingests some bedding it will be the end of the world, but a lot more have no issues with it. Aspen is a great bedding, I used to use it.
2. The OP stopped using aspen and started using paper towels, so I dont see where you guys are getting the urge to tell them to switch when they already did.
3. Temps are fine, humidity seems fine, if the stuck shed doesnt come off in a week or so I'd suggest soaking in warm water for half an hour or so and if it's just on the body you can gently rub it after and it should come right off if it doesnt in the water.

What size is the snake? Hoppers to adult mice are good if it's not tini-tiny, use the widest diameter of the snake as a set for you widest diameter feeder. You may want to add a second identical hide. Try blocking out 3 sides so that the snake is more secure (this doesnt seem necessary in your case but is always nice in a tank). Use aluminum foil on the screen lid to aid in maintaining humidity (1/2 to 2/3rds the lid).

Where are you getting your temps? You need to test the glass right on top of the heat mat, it could be getting to hot (but if you have a 5-10gallon heat mat chances are it wont, but it can). BPs dont seem to bask often so a heat lamp could be overkill and may not be necessary, but if the belly heat on the pad stays where it is and the ambient temp stays where it is you should be fine and may well just keep the heat lamp.

Aspen is fine, paper towels arent necessary, you can spot clean aspen, but with the towels you will need to pull all of it and put in a new set once a week/every bathroom use.