An easily, low tech solution to the problem of little bits stuck in the holes is to use bakery tissue (like you see in the stores to handle donuts at serve yourself bakeries).
Place a piece of bakery tissue next to the cutting face of the die then layer your cs and die cut as usual. When you are all done, most of the pieces will fall out on their own. A nice tap on the table will usually loosen a good portion of the rest, and the few remaining will flip out easily with a gentle poke of a pin or piercing tool. The tissue acts like Teflon on the face of the die and keeps the cs from sticking.
Hope this helps with the problem!