Well, I struggled some more days.
I found an acceptable workaround, which I want to share here.
In my tube model, I created 2 extra half-circular solid bodies and applied the decal on both of them, and the distortions do not appear anymore.
The decals appear also correctly in the drawing.
If you want to appear the decal(s) in the BOM, than the best way is to create completely separate Parts with the decal on it, and insert it as a Part in your Assembly.
Another advantage: you can also apply dimensions to the decal in the Drawing.