First, let me say I am not a Mat Cutter, but I cut mats. Meaning I know enough to pinch hit when the real Mat Cutter is out (that's why the hatchet and not the sword).
Our Mat Cutter used to use an F2100. Aside from how to slice it, you really need to experiment on your entrance and exit points.
Your overcuts (on the backside, because there is really no excuse for an overcut on the front) will be at different points. Just as it is different on foil board.
Make a small card that actually sets out the distance over and past the mat opening line and blade depth for different materials like regular board, foil, 6 ply, 8 ply, 12 ply (3 boards stuck together), 1/4 inch f/c, 3/16th f/c and leave space for new materials.
Now our Mat Cutter uses a Gunnar. A push of a (virtual) button on the screen and blade speed, depth, and overcuts are ready to go. Just drop in the board. The same for foil, moorman, f/c or whatever.
Wahtever CMC you get, if you do, I would strongly suggest one that is able to cut more than just regualr board. And do it well. Just like your old Hand cutter.
BTW the new Gunnar will cut bevel and straight edges. Very cool to see.