Thanks for the file, ag4medien.
If I had to do it for production, I would retopologize the mesh with the Pen Tool and go from there. This new mesh would have be a lower dense mesh and easy to adjust.
https://www.cineversity.com/vidplaytut/polygon_pen_part_07
The Upper object “socken” is based on a few un-connected meshes, which creates the main problem to find anything fast. I went through a lot of options, but pretty much any had a problem.
The most promising was with a plugin “UV to Mesh” which doesn’t work anymore on R20, so I tried to get a nice UV established, to work in R19. Also, here the mixed objects (collar and seams) created the main problem, I was not able to relax each while keeping the positions.
I tried UV projection, Wrap-Deformer, Cage, and Spline Deformer, none were able to do what was needed. The Ray collision didn’t work either. I had hoped to project it to a flat (but bent) surface and go from there.
The Surface Deformer should work, but the mesh ‘flashed’ from time to time. See file: [updated, a higher mesh density removed the jumping/flashing]
https://www.amazon.com/clouddrive/share/77wDq1wCD6GZGFXf3RHNuRuVLqBo4Dvnp0LCGAxd8Hh
Not completely flat, but very close.
Somewhere in the back of my head, there is a piece of information that a plugin can roll it out, but I can’t find it on the web.
What I did was to use five Bend deformers (the sequence and restriction is the key here), and flatten it out as much as possible (well, I could have done more with four extra deformers).
I used then a Current State To Object command, to get a copy. This object was then rotated and scaled to be flat. With the Magnet tool, some of the edges were smoothed out.
After that, I used a Pose Morph, set to Points, and dragged the flat object in, switched all deformers off, and the result is in the file below:
https://www.amazon.com/clouddrive/share/XLnvGSxPW0SuSNGc48iTByTR5j97IoU1SPwEiCm6BmR
I hope that the fly in has enough speed/motion blur, so it feels OK; otherwise, you can put a little bit more work into it.
All the best