Looks like the consensus of responses say don't use Azure.
Still, if you have something you'd like to keep and transition to Amazon/Other, that would mean getting into the Guest OS (one of your Moodle VM#) and backing up the code + getting an SQL dump from the remote MySQL server + an archive of the moodledata directory.
Am guessing the VM#'s are linux so there is also the possibility to use tools like rsync to get code + moodledata to new hosting environment. And there is a tool built into Moodle (experimental me thinks) that could transfer the DB from current Azure hosted DB server to a MySQL DB server you point to.
2 cents.
'SoS', Ken