Keep in mind I'm no expert but I'll post what I recently did and maybe get some more expert comments going. Besides, I'd like some critique on what I did.
I just went through a similar process in a bathroom after removing wallpaper from unprimed drywall (which made the usual mess). I lightly sanded (with a palm sander) as much paper as I could that was protruding from the drywall. Then using about a 4" drywall knife, I made a veritcal run down the wall with the mud, skipped a little over 4"'s and did the same, repeating this over the area to skim coat. After the first application dried I came back and filled in the cavities created on the first pass and rough smoothed it all with a wider knife. In affect, I was adding roughly 1/16" to the drywall and feathered it out as I approached molding, etc. It's easier to do a relatively small area at a time since the mud will dry out quickly and I can't imagine doing a large room this way but something along this line might help. I'd try a small area first to see what the results are for you.