Posting in here as well since I'm in a similar boat. Tried various of the assorted fixes scattered around (verifying steam cache, run as admin, compatibility mode, playing with graphics settings, disabling anti virus) and have come up empty. At first I thought it might have something to do with trying to play with AI settings, since I used to try and actually select an AI difficulty, the first time I left it at default it allowed me to play 3 or 4 battles before inevitably crashing to desktop after I let the game's auto battle take over.
Was able to submit all of my error dumps so hopefully that helps fix this. As for system specs: Win 7 64-bit, (currently) 8gb RAM, i5-3570K, Radeon 7870HD, all stock settings.