I have been using self built email servers for years now on Ubuntu Server with Postfix + Dovecot.
Once before, I have decided to build a newer email server, and I called it by a different Fully Qualified Domain Name than the Old Server was called. Then of course when the moment of switch over came, I had to alter the Resource Records (A, PTR and MX) in my domain (and at my ISP) to make the switch between the two servers.
The way I remember now, it is something like it wasn't really a smooth switchover, even though I have prepared all the involved Resource Records to have 1min TTL set for a while, it just didn't work straight away, without sweating a lot :).
Also nearly every single email within one folder of emails seem to be contained in a single file surrounded by all sorts of hash and checksum looking data, that made me a little frightend to copy emails from the Old Server to the New Server by linux file transfer. So, at the end I realised, that once I had both servers hooked up to Thunderbird through IMAP, actualy both containing the same account, I could just drag & drop all my folders from the Old Server to the New Server.
How do experineced people change over to a New Email Server?
During my last successful migration project, I used dovecot replicator. It can transparently replicate mailboxes between two servers, no data loss. You can take your time between the following steps, 0 stress:
Note: Replication is not real time but depending on your hardware and network it can be close to it.