Here is a before picture of our dining room, carpet and all! Whoever hung this wallpaper was really good at their job.
I've been filling a spray bottle with 3/4 really hot water and 1/4 vinegar. I spray the paper until it's very saturated. Let it sit for awhile (but not so long that the paper dries out) and peel off the top paper layer. Spray again and wait. Then I use my handy dandy Giant bonus card to scrape off the "gluey" layer.
If I could find more than 15 consecutive minutes to work on this, I could finish in a few hours. That's not happening, so I'm hoping to be finished by the end of the week.