I have send the email with the report, removing all but the most recent savegame to keep down filesize.
The only active protection being run while running Divinity was Windows Security Essentials.
My videocard is not overclocked, but after browsing a bit more through the forums it does seem that several peoples issues are traced back to the R9 290 series.
My girlfriend is now hosting the game, so when i crash i can get reinvited again, and she has the R9 270. She has had no problems at all.
Also, i had already tuned down graphical settings a bit to see if that would solve the issue. And i already tried it with Ambient Occlusion off, which made no difference. I have even turned off V-sync but i havent had the chance to really test if this had an impact on the problem as of yet.