Been experiencing similar problems, I thought it was AV not getting on with EAC, but I turned it off and it still eventually BSOD... although it starts randomly with the KB no longer responding, I can see the game going on around me, just can't move, then the game ends with BSOD.
Having tried 3x AV I think I've stumbled on the problem- it's the Firewall rules has gone squiffy, it's full of the same rule. Anyhoo, defaulted the FW rules (a clean 12 ish rules after default). Started the game, I got so far, then game crashed out (better than BSOD) but I got the FW rule asking if I wanted to let BF through (I said yes yes). Restarted EA, then BF, it's been running fine since even with AV on.