Ok, after testing it with the old spiral wrap, which worked, I asked the Prusa support if there is a trick to get the wiring harness in. They only suggested to wrap it tighter. In the end I got so annoyed, I took some pliers to squeeze the clamp together and that worked.
Still, would be interesting to hear, if one of you had the same issue. If not, then maybe something is wrong with the Rambo cover I printed.