Good day,
Are you still want to solve this problem you have, I can fix it, but of course not for $30, it is a little costly, but can be fixed and work perfectly.
When it works fine, any user that have access set on LDAP or active directory, will be able to access Moodle without login and get the correct access to Moodle.
Please let me know if this suitable for you.
Regards,