I've heard of a technique for dealing with the large amounts of stone is something about a single tile being a trash can for everything. How does this work?
You designate a garbage dump zone in only one tile using i-g.
Then you give the order to dump the stones you want to dump, or use mass dump: d-b-d. They will all be stored and forbidden on that one tile. To use them you'll have to unforbid them or use mass reclaim: d-b-c.