I don't think you would have much luck with carving MDF with a Dremel. The drywall compound idea is better.
Another approach (which isn't as crazy as it sounds) is to glue on individual "stones" made of thin slices of pink foam insulation. I have never done this with random stones, but I have had good luck doing it with cut stone:
The pieces were sliced using a razor blade. You could easily start with pieces like this and cut them to shape after slicing. Either that, or make several "sticks" of foam of different sizes and with different profiles and then slice them.
Nothing simulates stone like pink foam.
