[Closed for now] Automating UV unwrap of a particular mesh

Let’s say I am creating the following object using Curve-Geometry-Bevel:

(the “sandwich” of layers along the curve). Then I want a second UV channel on it, to go like this:
strand uv 2
,so Y coordinate of UV2 will serve as height coordinate of layers. (Wanted to use it with the hair material which utilizes 3d noise texture as opacity mask). Of course it can be done manually, but with complex object made of multiple curves, like whole hairstyle, this will be too much work. Is there any way to put UV information on the cross section spline?

Maybe: Make a second UVmap, switch to side view, edit mode and UV → Project From View (Bounds) ?

Would work with the simpler object but not a hairstyle composed of many multi-layered “strands”. A pity that Bevel cross section curve cannot contain UVs or vertex groups/colors

Perhaps I’m approaching it in backwards way. Maybe better solution will be to first model a whole hairstyle as 1 layer, then consecutively duplicate, shrink/fatten, and unwrap all the extra layers