It works! Thank you so much for your time! I'll take this as a Christmas present :D
My guess is that it's the free resize that fixed it. At first it didn't work, but then I tried my old resizing trick and it worked. Fiddling with the settings after "fixing" the display usually causes it to relapse (as with the other games), as does quitting to menu and going from menu to "continue" or "new game" or using alt+enter. However, in all cases, there is a chance for it not to relapse, which means I can also run it in fullscreen when the dice roll right.
I'll also note that the demo doesn't have any display problems.
Out of curiosity, is there any downside to allowing free resize, in Unity games or in general ? And what is the purpose of the "keyboard only" setting ?
Thanks again.