A friend at AAC instructed me to soak the parts in mineral spirits, which works. I find it works better if the spirits are cut with about 10% Hoppe's No. 9. For pistol and rifle cans that do not allow disassembly, this works well. Soak them for a few hours and blow the residual fluid out with an air compressor.
22LR cans are a bit different. Due to the lead and powder build up, the baffles get coated with a very hard to remove film.
My own personal experience has been to let the parts soak for 8 to 10 hours and then scrub them off with a plastic cleaning brush. However, there is a caveat. The soaking solution turns rather caustic after this period of time.
Early on, I allowed all of the parts to soak (baffles, tube, and end caps). When I let them sit overnight, I found the paint had been dissolved on the bottom of the tube that was in contact with the sediment at the bottom of the soaking dish.
AAC was nice enough to refinish the exterior parts at no charge, but it was not a nice learning experience.
So needless to say, I now only soak the baffles, and clean the tube and end caps with some WD-40 or CLP.
Personally, I would like to find something that does a little better job removing the crud from the baffles than my current technique provides. So I will say tuned to this thread.