In answer to your question #1 if I understand your description of the problem that the check is being pulled back down out of the die. I've only seen that happen if I don't pay attention and short stroke the operation. If I run the punch all the way up, until it contacts the die, the skirt of the formed check springs open and catches on the lip of the backbored clearance hole and is stripped off the punch.
The other problem could be using much thinner stock that can't spring open enough to catch the lip.
As for the Rockchucker difficulty I suggest investing $25 and getting a Lee press. Its probably easier and cheaper than designing a work-around.
Good Luck and let us know how it all works out.