Another approach that seems reasonable to me would be to install a brand new Moodle site and to customize it as needed, then make a backup of all the categories and courses from the old site and restore them to the new site. But maybe this seems like too much work. If I had to do it I would have tried to do it from the command line, using `moosh` and possibly writing any shell script to automate backup/restore.
However I am not sure if a course backup made in version 2.7 can be restored properly in version 3.3. Also I am not sure if a course backup includes the data files as well.