I finally managed to log in to one of the servers, yay! Solution: Opened Arma II Arrowhead in Admin mode and joined a regular Arma II Arrowhead game. This updated the BattlEye client, which might have been making troubles behind the scenes. Afterwards, I closed it down, opened the Six Launcher normally, and I could get past the Loading screen. Hope this might help some of you with the same problem (although there are probably many different cases that produce this error).