Is the plan for migrating a mail server from one physical server to another correct?

Question

Mail server

There is an IceWarp mail server and the need to move it from one physical server to another. ip is changing.
There are more than 100 clients on the server, and in the process of transferring and updating DNS, you need not to lose letters that are not synchronized. IceWarp has a migration utility that simplifies the process.
As I see it -
1. We register all MX domain names with a record with priority 20 (greater than the current one) on the new server. At the same time, the second server does not accept letters. Those. letters go to the first server.
2. On the first server, I migrate everything to a new one
3. On the first server, I disable pop3, imap services, synchronize what has come to this server at that moment (it takes about 10 minutes).
4. On the second server I include pop3, imap. Those. now the storage of letters and their receipt by mail clients will be from the second server. Through the first one, only sending letters will be sent if someone has the same data.
5. I update MX only on a new server.
Is it a good idea or did I miss something?
Do I understand correctly that if the MX server with the lowest priority is not available, then mail services will simply go further by priority?
Thanks