Wrapping tread accurately around a tyre - possible?

I've been attempting to wrap an accurate tread pattern around a tyre, but the results are unsatisfactory. Check out this document:

https://cad.onshape.com/documents/589323adb204b50ff2cad640/w/841a281b817a68bea31e61fa/e/4e0c720dc39bd17743dda3b0

If you look at Version 1 of the document you can see the 'valleys' of the tread are stepped, and not consistent in depth. This is because I cannot see how I can map the basic tread sketch pattern onto a curved surface.

If you go to the Main version of the document you can see the problem. The sketch is flat, and the tyre surface isn't.

If I could just map a sketch to a curved surface accurately I could then thicken it and boolean it with the tyre, but I'm falling at that first hurdle.

Other than turning my brain inside out doing extreme 3D construction and projection/intersection of curves to compute a curved tread starter pattern, does anyone have a manageable method of producing an accurate result with consistent depth tread throughout the tread pattern around the tyre?

I looked for a FeatureScript which might help but didn't find one.

Is this functionality likely to be coming to OS any time soon? It seems OS needs a new set of tools for things which are not simple geometrically.

Cheers,
John