I wound up doing what I originally intended and it worked out fine. There were one or two paint bubbles after the first coat of mud that I cut out and patched, but other than that there were no problems.
Basically I removed as much as I could first, then I sanded and did two coats of mud. Rather than sand, I used a wet sponge between coats (you can do this if you're very neat applying the mud). I then sealed it with primer, painted, and finished off with a rag texture. It looks great. Im on to bathroom #2 and I used a wallpaper removal gel and special tools that made removal a snap. Available at any Home Depot. The walls are in much better shape this time (hooray!)