In reality, when a miner digs out a 7x7 cube of stone, 343 cubic feet of stone are left behind in smaller chunks. Sure he breathes some in as dust, but that's hardly much at all.
For every miner you would need people to haul out stone, otherwise the miner would throw stone behind him and fill up his work space.
If we assume a single stone can wall up a single cube, it must be at least a foot thick and 7x7, so 49 cubic feet. This is equal in volume to a liquid at 1/7. It also means there was debris equal to 6/7 that magically disappeared, but let's not dwell on that.
So we have 1/7 volume per stone. It makes sense that a dwarf can scurry overtop 3/7, right? His movement would be slowed, of course, when passing through that square. Missile weapons passing through a stockpile that holds 3/7 or more stone should have a chance of striking the pile and breaking, such that 7/7 piles automatically block line of sight and missile fire effectively counting as walls themselves because they'd also block movement. Should they also block flows?)
Anyway, you could simplify it by just letting stone stockpiles hold 3 stones per square, and halving movement through the square if it holds more than one. The pile would fill up each square to 1/3 completely before filling up the next layer above.
I think Toady will eventually get rid of quantum dumping. So gird your loins!