Whoa! That is awesome!. Share away. I know a lot of people here love seeing projects and seeing some that are altruistic makes it even better. 
I was just putting together a nintendo labo kit with my son this last week and cardboard is a very impressive material. I think most of the boxes we use are made in such huge quanitities that they are stamped with big cookie cutters. I have also seen a lot of cardboard cut with lasers. In a similar vein, the “dollar tree foam” is a popular medium for RC airplanes (check out flitetest.com) and a needle cutter us a great tool for cutting and perforating that. So that may be worth a try.
Newb looking for some advice to get started
@focusedonsound is also hoping to use it to mill Coroplast, which looks like plastic cardboard to me.
I would make an uneducated guess that the cardboard may be too soft to be cut with a mill. But it may depend on the feeds and speeds. If it gets too “mushy” it will feather a lot instead of cutting. Have you tried cutting it with a router? I know some people do mill foam, so maybe it will be fine.
As for sandify, it really isn’t the right tool for this job. You could easily design some texture with it, but if you want to share the cad and maybe make it parametric, I would look into onshape. There are some sheet metal tools included and there is a kiri:moto package for doing the CAM. But even if you just adjusted some variables and spit out a dxf, that could be used to cut it out on many platforms.
This seems like an excellent application of the tech and I love seeing use of more compliant materials (instead of trying to make a seat from metal or plastic).