Ok, so the problem is with the games themselves, and not the saves. Beyond Divinity is using a modified version of the Divine Divinity engine, so both being effected isn't surprising.

Did you update your video drivers, or anything like that, before this first started?

In my case I don't need to play the game at all to trigger it, just have the computer running continuously for days.

In the install folders for the games, try right clicking on the div.exe program file and select properties, then switch to the compatibility tab and try checking off Run as administrator, Disable desktop composition, and (if applicable) maybe Disable display scaling on high DPI settings. You could also try different compatibility modes.