If your local Moodle is only for course development, it doesn't make sense to migrate the whole site to you hosted Moodle in the Internet. Instead transfer only the content coursewise. Backup the course https://docs.moodle.org/en/Course_backup in the local computer, start a course restore https://docs.moodle.org/en/Course_restore in the hosted Moodle and upload the backup when requested.
Note that the two Moodle versions may even differ, but not too far!
P.S. You are in Moodle since 2007, so you know this. The answer is for others who happen to find this discussion.