Hi everyone, I am back to give probably my last update on the situation, as I have found a working solution to my problem.
This being said, I still couldn´t get the 1080 Ti to work but the 2070 Super I borrowed just worked out of the box. So in the end I bought a used 3080, hoped that it would work just as well, which it does. Therefore a workaround had been achieved.
Also, ASUS’ first level support (somewhat expectedly) didn´t really seem to grasp the problem and suggested that only Windows systems were supported. They would be willing to forward the issue to the second level if I did testing in Windows which I already demonstrated to be working. I have since offered to send them the problematic 1080Ti for testing if they were interested in investigating the issue. However, I don´t really expect them to pick me up on my offer. But hey, if they are going to make me eat my words, I will gladly update this post.
Thanks everyone and peace out 