What unpowered bladed tool can make deep beveled cuts in sheet material?
You could make some utility or razor blade holders from wood. Saw a rectanglular block down the length at the desired bevel angle, clean up with a hand plane, then clamp the blade in the centre using predrilled screws, from both sides.

You can then use it by drawing it against a fence, either plunging like the mat cutters or starting from the edge of the material.

It would be inexpensive to make a few standard angles; you could extend the range by placing thin shims along the part closest to the fence to achieve steeper intermediary angles.