Hi,
I believe there are two issues here, stacked onto each other.
First is a problem with latest Linux release and 1366x768 resolution - mentioned here:
http://displaylink.org/forum/showthread.php?t=65022 - you could try an earlier 1.1.x release, which should still work on 16.04 kernels (if not - compile the latest evdi sources from github manually, and use the rest of components from 1.1.x release as-is).
The other could still be, not enough power delivered.
I have tried this internally - took a build without the 1366x768 problem, and connected the screen through a powered hub with a short good quality cable and it works - see attached photo.
Regards,
Michal