Hello TeT!
You cannot copy the weight values from one mesh to another.
You can duplicate the mesh and possibly readjust it manually to achieve this.

Two suggestions:
You can now pack your meshes with Polygonal texture packing to automatically save space where possible without having to rotate textures manually. Texture Packing - Spine User Guide: Output
Blog: Spine 3.8 released: Polygonal texture packing

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You likely can achieve the same bending results with fewer vertices. Try to cut the number down a little, this will make the mesh more manageable and improve performance too.

You can view your mesh not deformed by bones by unchecking Deformed in Edit mesh mode.
Meshes - Spine User Guide: Deformed

Unfortunately, I just tested it, and you cannot rotate the vertices, only translate them to a new position.

What you can do is manually reposition each vertex instead (with Deformed checked so it doesn't wreck the mesh)
Therefore, I think your best bet is this:

1. rotate the new mesh (which could be a copy of the old one with the new artwork inside it) so it matches very precisely the old mesh
2. select one or more vertices from the old mesh and press CTRL+C in world axis
3. select the corresponding vertices in new mesh (in the same order if you're copying the same ones) and press CTRL+V

This should be reasonably fast and painless to do, but still, a hassle if you have many vertices. At least this way you shouldn't need to redo manually the weights :>