I just tested WhateverGreen with Mojave public beta 2. The artifacts seemed to start showing much faster, but seemed slightly less intrusive for some things. Previously when the artifacts would appear, the menubar text and drop down menus would be unreadable, but so far that hasn't been the case with WhateverGreen. The artifacts aren't staying on the menubar permanently, but they do seem to be permanent on the drop down menus. I can watch a fullscreen youtube video in Safari without artifacts (although they do show up while the video is switching to fullscreen). I only tested for maybe 15 minutes so it's possible that it could get worse. For me, any amount of artifacts is unacceptable so I wasn't interested in testing any further.
I've setup an High Sierra installation to test it. It seems the glitches are far less than usual for me. It happens slightly less, and it's exactly the same situation you described. Just for the record, here's the setup I've tested so far:
MacOS High Sierra 10.13.6, CUDA Driver 396.148, Nvidia Drivers 387.10.10.10.40.105, WhateverGreen 1.2.0.
Update: I was testing some stuff here. If you keep a game fullscreen, the glitches doesn't appears anymore, but is just a matter of changing to window mode and the window will be entirely glitched. I've close the window and there's no glitches anywhere else. In other hand, if I open youtube in Safari, changes to fullscreen to window again, is a matter of minutes to glitching and transmit to menus and other windows.