The design of the second side will need to be positioned accurately regardless of when the cuts are made. If the camera-based alignment needs cuts made in the first setup to register the second setup, and if the rectangular perimeter cut isn’t sufficient (because the accuracy is so abysmal in the periphery of the image) perhaps adding two small features into the middle might be helpful. For instance, two small circular cuts in the waste material could be used to align the second setup, and if they’re in the center-ish of the camera’s FOV, they should be just as good as using the tokens.
Takitus has said that he puts tape down on the bed and then engraves lines onto it as a quick and dirty (and effective) alignment guide. In a situation where a fixture is required, that sounds easier than trying to use tape to reattach every batch of tokens after cutting them out in the first setup.