My students use acrylic paint on the no-stick pallets and do not clean them-- it dries and we add more. At the end of the day we spread it all over the palette. Over a semester it builds up a nice layer and I carefully peel it off. We're making jewelry with it right now. This would be great to cut up and collage. It would look like a heavily textured carved painting. It keeps paint from getting washed down the sink and as it is reused I don't feel like so much is wasted.
For my own paintings I sometimes use light modeling paste which, When dry is very easy to carve with lino tools before painting.