On thinking about the issue, wonder if you wouldn't try something ...
In the 3.0 instance, pick a representative course that has SCORM/Videos that work/play and make a full backup ... includes users, all resources. Backups do NOT use .sql for DB info but XML. Upon restore of a backup XML converted to SQL.
Take that backup and restore it to the 3.5.x. Now when you restore bring it in as a new course ... don't try to replace what's there. Do put it into the same category ... let moodle decide the course name to have 'copy' at then end of the course name. That makes it easier for you to know differences in courses.
See if the restored course works or not.
If it does, great! But then you probably need to undo whatever you imported table wise. Too massive and very prone to human error if you are not a DB 'guru'.
How many courses does your site have?
Again, is the new hosting Linux or not? If so, what distro?
IF the restore works, then there is your path/process, but suggest wiping out the 3.5 you have, install a fresh 3.5 with only categories setup so that when importing backups one can place courses back into the same categories.
If linux, one can restore multiple backups to a category using a command line utility called moosh. I have moved a site of over 4000 courses into 20 categories (new site affectively a clone of the old) via command line using the backup.php script in old code, copying the .mbz files to new server in a file system on new server, then moosh to restore all the courses meant for a category. NO issues with those course restores.