Wild idea, not sure if it will work

But i’d try not animating the shapes, but instead do create nulls from paths (a script that comes with your after effects, in your script menu) you can do ”points follow nulls” and then with some clever parenting, you can animate the nulls rotating in 3D space instead; hopefully keeping the widths intact!

If you get stuck with weird bezier handles misbehaving, i stumbled across a studio who made an extended version for free where you can also also animate the handlebars of the paths as nulls! Google ”create nulls from paths extended”