Agreed with Krabby on riv nut inserts. I'm not sure how thick the dash plastic is, but alternatively, could something like a Toggle anchor work in an application like this?
https://www.amazon.com/dp/B011352954/?tag=globalgrena0b-20. It's made for drywall, but as long as you drill holes and place one in each corner of the mounting plate, I'd think it would be pretty solid. Also, use much shorter screws, than what's shown in the link.
Also, I've never 3D printed anything, but is it possible to apply a texture (similar to that of the dash or the original mat) to the mounting plate? It would make it look more OEM.