I'm having the same initial problem. When I delete all the files in the Battleeye folder, Im able to start OA, see my server in the multiplayer directory and then when I try to join my server I get Battleeye Initialization failed.
When I back out of the Battleeye directory and nav back to Arma 2 Operation Arrowhead\BEsetup and start that exe, it will replace the files in Battleeye folder but then I go back to having the command prompt with it failed there again too. It seems to be either that set up file is writing corrupted files or maybe it's now allow us to connect to the Battleeye server at all?
It' doesn't make sense. I was logging into my server just fine this morning but after a restart this afternoon and me trying to log back in later I've delt with this. I've tried total wiping of all traces of Arma on my system and did complete fresh installs and still same results. Is this because of the gamespy migration?