Something else you may want to try, since you mention 1000 other parts, would be to make vice jaws that are the length of your part. In your picture you show 2 vices,so you make step jaws as long as your part,your jaws are then bolted to just one vice and the 2nd pinches the jaws. This way your stock is held the entier length and can be changed in and out quickly. However this does only work if you stock is straight to start with, (within reason).Just a thought
Just push the button,what's the worst that could happen.