The next thing I wanted to try was the "paint palette" idea that Jeff suggested. I usually use old yogurt container lids as paint palettes, but the idea of using part of the tabletop as a palette was intriguing.
So I again commandeered the kitchen table, set up the hobby mat, and prepared to finish priming some dungeon pieces. Then I squirted some black paint right onto the tabletop...
...and started painting the pieces. Surprisingly, as I used more and more of the paint, and added water to it from time to time so I could work the paint into the crevices in the scenics, the "mess" almost cleaned itself up!
So I tried to be messier. (Actually, when using this large of a brush, I usually manage to splatter the paint around my working surface!) At last, the pieces were primed...
...and I had a "messy" hobby mat to clean up. There really wasn't much to clean, as even if you directly stroke paint onto the map, it tends to bead up. Although, ever so often, something sticks - the "white speck" in the foreground, for instance, is a tiny bit of plaster that is "glued" to the mat by a bit of paint.
I tried wiping with a dry paper towel, and 99% of the paint wiped right up.
I then tried a damp paper towel, and most of the remaining specks of dried paint came up immediately.