I could be wrong but Im not sure if a laser will cut that material well. We cut ceramic wool blanket by hand like you are doing but its easy shapes like rectangle strips. For curved pcs or with holes and cutouts the use a waterjet (without abrasive) and it works great. We use a pc of foam insulation board on too of the slats to support the bats. If you do it right it doesn’t saturate the matt with water. Sometimes tho it does get wet and we let it dry out overnight.
If WJ doesn’t sound appealing Maybe Check out the CNC cutting machines made by Gerber or Eastman.
https://www.gerbertechnology.com/gerbercutters/
https://www.eastmancuts.com/automated-cutting/