Enrolment

That would probably be the best. I don't know if there's a way to set system-wide roles for new users based on their LDAP context; it might involve some more Moodle hacking I'm guessing though

I don't know what would happen if an entire group of professors was defaulted to "teacher" or an entire group of students was defaulted to "student;" I'm guessing that the students would be a "student" in all courses and the professors would all be "teachers" in all courses. Which definitely isn't ideal for us since we have about 6,000 courses and 37,000 users in the system

I don't know what your intentions are or what you use Moodle for, but that might not be the most ideal thing for your situation either unless you want all the students to be a "student" in all the courses; generally global roles aren't the best thing because they are truly "global."