So I don't know how I screwed up this bad, but I did. However, I am seeing if there is ANY way to get around this.

I got outguilded from the mages guild three times. I managed to not notice, or forget, or any combo thereof, during the course of my playing. I hadn't even started the main quest yet (was working on going through the other factions). Tar-Meena never leaves those archives or sleeping quarters. Is there ANY was to get to her? I tried slipping on the cowl of the nocturnal and pickpocketing everyone before i get kicked out of the tower and guildhalls, but the arch-mages key doesn't do anything worthwhile and it won't let me keep a mages guild key. Any ideas?

Three strikes your out. Start over

He's right.
The mage's guild is strict that way.
Your current character cannot access the guild again, there's no way around it.