I think Adam mentioned something in the works im the semi distant future for this, capability to migrate between enhance servers.
But, what I would do is what I do for most migrations:
ssh into server 1, zip wp-content, dump DB or use plugin to backup DB depending on the situation (sometimes updraft is just easier, meh).
Setup the new account/site on server 2. Ssh into server 2, use wget to download the wp-content zip file from server 1 + the DB dump. Delete the installers default wp-content, unzip my downloaded wp-content, restore DB, chown everything since my root login prolly messed up ownership.
And that's it, it's ready to update DNS. Migrating a 1GB site is like a 5 minute job.
If I used a plugin for the DB backup for some reason (like the site is 40GB and I just want to get other things done while those files are zipping/unzipping), then I'd update my computers hosts file with the domains new IP so I can login to the newly setup site on the new server and work on the migration without affecting the live DNS. I'd update the control panels default DB to use http in wp_options table, just so I can login and run DB restore with updraft without getting https errors from browser.
I've actually been migrating most sites into enhance this way so far, all the sites that are over a couple GB in size, it's just faster than manually uploading things with my home internets 20Mbps upload speed, when I can use my server to download files between servers at 1-10Gbps.
