I was also thinking of adding a small humidifier to my house because the air is just so dry these days. I am in Illinois, so I feel ya.
As for the shed on the back, you should be able to pull it off after you give the snake a 20-30 minute soak in a closed container (with air holes). I usually use a wet paper towel and just roll it off, front to back. The snakes hate it, but it gets the job done!
And really, as long as there isn't any shed going all the way around the whole body, the snake should be fine. Hopefully the next shed takes it all off!