In all honesty, really intense groups on campus like the ones you described are almost effectively unhoused local GLOs without rituals but with a very specific purpose. If you want to join an actual GLO, you're gonna have to drop one or two of them so you can actually fit it in.
Now, about being "shirted" -- I've never heard that term being used either, but AFAIK, on most campuses, the sororities who do not reach quota will do COB and informal recruitment in the other terms. That's when they all have their individual recruitment events. However, it's up to you to find out about them unless you have a friend in a sorority, etc.
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