it seems as though the best way to do so would be to move to a new server at the same time so that I'm running on a supported version of CentOS.
I guess you misunderstood the announcement, we will continue support iRedMail servers which running on CentOS 5.x. But for a new iRedMail installation, you have to choose CentOS 6.
Personally, i think upgrade from iRedMail-0.7.3 to the latest 0.8.5 by following our upgrade tutorials should be easy enough. And this is the best way to keep your iRedMail up to date.
1. Should I upgrade the current version on the current server first, and then move to the new server running Centos 6.4? Or,
2. Should I install the latest version on the new server and then try to move? I'm concerned about changes along the way in the MySQL databases.
And we have a basic tutorial to help you migrate to a new iRedMail server:
http://iredmail.org/wiki/index.php?titl … ail.Server
The most important thing is, making sure you have the same SQL/LDAP structure.