Cardboard shouldn’t be an issue at all. Were you looking to cut 4mm thick sheets also? I would probably start with something like 20p, 50s, 20f with air assist. When testing vector cut parameters, place some scrap material underneath. The right settings should only lightly mark the material underneath.
Let us know how you go and we can add the settings you find to the materials list.

Hey Ben, I’ve found a lower-cost solution that achieves the same floor covering effect at a lower cost and with greater flexibility for storage: yoga mats! I also got word that my EVA floor mats couldn’t be delivered, so I’ll hold off from the laser cutter experimentation for now. Thanks!