As far as mounting the ribbons and medals (design considerations aside), there are two type that we regularly encounter.
The “ribbon/shield” type with pins – just puncture the mat board with the pins and reapply the clasps from the back.
The other type – cut a thin slot slightly less than the width of the pin into the mat board. Loop a piece of fabric, tough paper or tape through the slot so that the doubled end is facing outward.
Run the pin through the doubled end, pull the fabric, paper, tape (whatever) tightly from the back and secure it to the back of the mat board with tape. Theoretically, the medal can be removed and repositioned later by undoing the clasp of the medal (as long as the doubled end doesn’t slip through the slot).
We have recently begun to use a product called EZ-Tach which makes mounting go a whole lot quicker. But in order to remove the medals, you have to essentially destroy the mounts, so one cannot consider that to be a good method for your purposes.