sync 3 mail servers

Hello good day.
In the last few months I have used Cwp and I think it is quite interesting. At this moment I have created a group of 3 cwp servers, which are behind an nginx balancer. Everything works fine for me.
The only thing I can't do is synchronize the emails between the 3 servers. e tried rsync in cron every 3 minutes. But here they give me problems, as the cron has to be with root later on another machine it does not recognize it, it does not have the permissions.
Bidirectional does not work with imapsync. And in this way, if you delete a message on server 2, when it is synchro- nized with server 1, it will put the message again. It's a mess.

Do you have any ideas? How can I synchronize the 3 mail servers? or is it better to use a virtual space for all 3 where the emails are stored? and so always each change is for the 3, but if I shut up the virtual space for nothing I have 3 servers if in the end it is the same space

Thank you

In my case, I don't need the 3 servers syncro in real time.
I have a script created, the cron call this script 2 times at day, and syncro all mails.
But only one server is the "master server mail", the rsync is from this master server mail to the others 2 servers.
When access to others 2 servers are the same emails of master server mail.