Yeah sounds like my rig. So when you set the graphics level in BF3 what is it set to? 1920x1080x120Hz? I have to drop down to 100Hz to be stable all the time else the screen blanks out trying to reset itself. Now I will say I am quite aware you shouldn't try that level over HDMI 2.0, only HDMI 3.0 can handle that level, which NVIDIA / ATI don't put out HDMI 3 connections normally (they defer to DVI-D connections instead). You could be overbuffering the HDMI making it fail - BSOD when trying on that. What happens if you try playing at a lower resolution? Do you run HW Temps while playing the game? What do you get (I am usually 80C)?
Last thinkg I might consider is that your running a AMD chipset but a NVIDIA card, that could be a conflict when pushing that hard. Normally people running NVIDIA stick with Intel, and only keep ATI on AMD, as that avoids conflicts in the driver levels (historically companies purposefully gone out of the way to NOT make a effort at cross compatibility, to force customers to migrate to thier product lines exclusively so this may be the problem with this case too and not identifyable on the surface).