My guess would be to mimic the new server, with the standard restore procedure. My personal favourite is the script below, ive used this many times to move my server (however always to the same os version)
[SOLVED] Yet Another Backup Script for Community Version
Then use the KiddieOS (Ubuntu) dist-upgrade procedure....then run the zimbra install, for the same version, again.... hopefully ending up with a working version.
Be fairly easy to test this in VMware first...