I don't know how minecarts interact with pressure plates, but what if the minecarts were sent to the shaft and guided back, with a pressure plate that only responds to dwarf weight that opens the hatch in the shaft to drop the stuff? That way, the hatch would only open when the minecart is definitely not dumping anything. It still might mean items dropping 1-z on dwarves if they happen to be standing under the hatch when it opens.
Or you could have a logic gate linked to the hatch in the shaft like this:
OOOOO
O_P_O
O_O2O
OBOAO
O3O1O
O = wall
_ = empty
P = bottom of shaft (hatch is 1-z up)
A,B = floodgate?
1,2,3 = pressure plate
Begin: A is open, B is closed. 1 is linked to B. 2 is linked to A. 3 is linked to A, B, and the hatch above the pile (possibly through an inverter).
Step 1: Dwarf goes to retrieve an object from the stockpile and steps on 1, opening B (both are now open).
Step 2: Dwarf passes through A and steps on 2, closing A.
Step 3: Dwarf retrieves object and moves toward B.
Step 4: Dwarf exits loop, stepping on 3 which resets the system by opening A and closing B, and opens the hatch (which apparently closes automatically after 100 ticks) to drop more goodies with no one underneath.
This probably doesn't work for the obvious reason that there's no way to ensure that only one dwarf is going to be in the loop at any time. But you see the concept.