It took me quite some time but I have worked out a solution for my case. Dovecot has a built in synchronization tool. Unfortunately that limits your "master" nodes to 2. It is not possible to run more syncs. That's why I am not using it.
There are 2 steps to my implementation:
1. The synchronization
I am running the pods in a stateful set. That way the names of the pods are more predictable. I created a side container running lsyncd (check out my repo for more details on how I build the container). Whoever wrote that tool, you are a genius THANK YOU. During startup of the pods I am providing some details to an init container such as how many instances I intend to run, namespace and service, and the structure of the ssh sync LUA file. This information is required for lsyncd to know what to sync with. I pass the LUA config into the container and add the names of the pods that will be available for the sync to the LUA script. As I said I needed name predictability. Once that init container is complete, the LUA script is built and ready for use in the lsyncd container.
2. startup of the containers
once this "prep" work is done the containers start up. The lsyncd container gets a separate 100MB shared pvc (outside the mail storage) in order to exchange the SSH keys between the containers. Assuming you are running 3 instances of dovecot, a process inside the lsyncd container creates a key, stores it on this pvc and saves it in the appropriate folder to allow the sync. The process is pretty much the same as logging into ssh with a key instead of a password. The startup script checks for the availability of the keys until all of them are found and stores them where needed. Once that is complete, each of the lsyncd containers creates a file with its number to signal key integration is complete and once these files match the number of instances the keys are deleted. At that point the lsyncd sync is ready and setup.
At last the dovecot container is starting and completes the startup process.
Should you have any questions please feel free to post here and I'll get back as soon as I can.