If you want a mule where both the coin inlay and the plastic ring differ from the original you have to work with one that doesn't have the two coins welded together. Some are, some are glued together, and some aren't attached to each other at all.

Frontier had a lot of mules made when the plastic rings were burned off during distruction. All the reconstructions I've seen have both coins correct, but inserted into a completely different design of plastic ring.