Thanks a lot for replying. Recent follow-up:
it turns out my dock was/is defective in some way. It's been exhibiting some really strange behaviour as illustrated by this video I've recorded for a support rep from i-tec:
https://www.youtube.com/watch?v=AVyk...annel=ekhangel
After recording the video and after a twentyth-or-so full reset of the dock it suddenly started working with any cable I have - despite the one original USB-C cable that it came with and that I have apparently damaged. With this cable, the dock gives the horrible lag shown on the vid.
All in all, it's a complicated and really boring story to an "outsider". But thanks for your feedback.