I just studies
DXF file formats not too long ago. It turns out
DXF does not support curves directly. It makes curves from a bunch of straight lines. I am not sure if DWG would be better but I think that format is similar.
I second the “have another” vector format supported although I personally lean toward SVG but either of the two you mention would be good too
I think IGES can do what you are looking for and in my very limited knowledge seems like it can encode 2D or 3D shapes. Still trying to understand it all.
Long story short maybe try to go from Illustrator to IGES (if you can find a converter) and see if that helps… A selfish ask is if you do try that, let me know how you fare on it would be very helpful info.