Try to put your desktop resolution in the same resolution you want to play. Does that fix that problem?
but any change in the resolution will cause it to happen before any major event
The game aways force the user to restart after changing the resolution in the options menu.
In the graphic options menu, make the game NOT use the menu in the desktop resolution. It will make the game use the same resolution into the menu and into the game, after the start it will not change the resolution again. Does that fix that problem?
It doesn't happen as often if I leave the default graphic settings on
Maybe there is an incompatibility between some graphic option and the vga you have. Try to find an "stable" setting. You said you have "2x 7950s", try to enable/disable the SLI, and see what is the diference in both modes.
If you run other mondern game in the same resolution you are runing Divinity 2, does that "black screen" also occurs?
Do you have any type of Antivirus? Try to disable then, does this solve your problem?