I cut into gearbox using a technique by Josh Gambrell here (but my circle has 16 vertices instead of 12 in Josh’s tutorial)
and after this the shrinkwrap technique again for smoothing out distortions. The shrinkwrap target uses one subdivision more than the shrinkwrapped mesh in order to remove even the most subtle shading issues.

Thanks to @spikeyxxx for this tip in the backhoe modeling forum here and thanks to @theluthier for his tutorial on this technique in the backhoe livestream #3 beginning here at 1:53:18.
The gearbox file is here.