So, I came into the resolution that making my space station rotate exactly 360° every single orbit around Kerbin was somewhat impossible manually. What I'd like to have in MechJeb is simply an utility to achieve this. Should be a simple button, that I can click in the orbit.

This so, that a space station, a satellite or a probe will always be positioned the same to the planet, making it easier to apply solar panels, etc. knowing that they won't be blocked by other parts of the construct.

Thanks for your time making such a great mod.

This is impossible, since craft rotation is not simulated “on rails” in KSP. If you leave the vessel (you don't actively view it) it stops any rotation (same as when you warp it).
You can however use the SURF option in the S.A.S.S. to auto orient the station towards the surface. Of course it will not rotate while it is on-rails, but as soon as you resume the detailed simulation of the vessel, it will rotate towards the surface. This comes fairly close to what you want.

Summary: What you want cannot be done because of how KSP works.
On the other hand: Using S.A.S.S. SURF option you can implement what you want to an extend, in that your vessel will resume the correct orientation when you view it.

Conclusion: Nothing needs to be done about this, as the functionality already exists in MechJeb, for as far as it is possible in KSP.

There is a mod that adds rotational inertia to the on-rails system. Vessels continue rotation through time warp and no longer loose momentum upon unloading into rails.

PersistentRotation is the mod