Track stops can be lever linked and seem to have no problem being built on ramps. Perhaps linking one to a pressure plate, with the cart sitting there. The ramp should impart speed to it, and send it into motion. Of course I haven't actually tried it but it's worth a shot.
You'd have to put it on top of the ramp. Somehow.
Here's a
simple idea that might work:
1. Set up a chamber with a hole next to it. The hauling route's first stop goes there, and tells the dwarves to push the minecart down the pit once it's full.
2. Before the minecart is placed, put a floor hatch into the floor and link it to a lever.
3. Under the floor hatch, put your minecart-acceleration device.
4. In case of attack, pull the aforementioned lever and report the most amusing casualties (of either side).