I suspect that I will be shouted down for the following but here goes.
If you have a Dremel along with either the Dremel workstation or Dremel vice then simply fix your Dremel in a horizontal position & attach a flared brass bristled brush. Without switching on slowly turn the chuck by hand and 'feed' the brush into the bowl. Then preset the speed to ~10000 - 15000 RPM. Holding the bowl firmly switch your Dremel on and move the bowl too and fro for about 5 seconds.
Check & empty the bowl often and don't run for too long. I have had much success using this method of removing stubborn cake and have yet to make a pig's ear of things. Patience & a gentle touch is the key here.
Regards,
Jay.