The issue is solved, thanks to the following hint:
I recently installed HS using onboard video then installed my GTX 960 with Nvidia web drivers and everything works great.
I did exactly that. Unplug my GTX680, connect HDMI to the internal graphics port, activate IGP in UEFI and set it to "boot first".
Then by using the IGP, I could upgrade to High Sierra without a hitch.
Afterwards, I just reversed everything and now I have a fully working installation of 10.13.3 without any further configuration.