Short answer is that you'll have to migrate everything over by hand - domains, settings, files, database, ssl, etc
For the database version changes, I did run into some issues trying to port over structure and data "as-is". What I ended up doing is setting up a new database, running the app migrations, then porting the data over (I used Navicat). This way the new DB structure would be up to date with the newer version of MySQL.
Once your new sites are back up and running you can point Ottomatik to your new server. I haven't used them myself, so I'm unsure of the process.