If you reduce your grit size, then it will get insanely smooth. If you get into the 100+ grits (140 feels like flour), it will leave a nice smooth smooth finish that paint will love. You can then use a rotary tool and some polishing grit on the paint itself (after it's well dried of course) to finish the piece.

I would actually be tempted if I had a home setup to try a few pounds of flour as medium to see how it works. This was just a brain storm, so something may be better, something that easily washes off, is easy to dry (probably not flour), and won't kill you if you accidentally inhale it.