Well, it's the year 2023, and it looks like it hasn't been implemented yet. We faced exactly the same problem during the private LAN session this weekend. There is no BattlEye (BE) disable option for private servers, and in the end, it's up to the owner of the server. We ended up refunding 16 copies of DayZ and had a ruined weekend that we were looking forward to.
Moreover, there are growing concerns about anti-cheat software, especially those operating at the kernel level. Instances of similar anti-cheat solutions have been exploited to perform actions beyond their intended purpose, potentially posing security and privacy risks. Users have expressed worry about the level of access these systems have and the potential impact on system stability.
If you have any luck creating and playing on a private server without BattlEye, please let us know. I really would like to play this game with friends without worrying about installing BattlEye and the associated concerns related to kernel-based anti-cheat systems.