Full-disclosure, this girl is certifiably nuts (which I kind of like in my own sick way), but I still want to have sex with her. I had a chance with her back in November, but resisted for a few reasons (girlfriend) at the time. Felt I was in the friend zone when she told me about a hook up she had a couple months ago and now they're "exclusive," even though he doesn't live in state. Ever since then, she has been calling and texting me at all times of day and night to get together. She just texted me for drinks and sushi over dinner this week. Am I completely in the friend zone, or can I get out?

Sounds like you only want to have sex with her, so who gives a fuck if you are friend zoned, unless you really value your friendship with her, which it sounds like you don't and you have no problem fucking a chick in a relationship, which it sounds like you don't then you might as well try. If you get shut down so fucking what you lose a crazy friend you clearly don't really care about anyway or she is receptive and you get to hit it...sounds like a win/win.

Crazy girls are fun, until somebody invokes a restraining order.

Start reframing some of her texts as sexual, putting it on her. Random shit like if you're meeting her and she texts "Coming!" push saying "You wish!", or "Easier than I'd anticipated"
Or "Hey what are you doing?" respond with "not much just masterbating in my bed" seriously you have to almost not even give 2 shits, take some risks push the interactions a bit in person and through text, 1 step forward 2 back don't over do it you'll know when she stops responding in which case just ease off.

Bro If you end up fucking her you will get too attached to this nut case. Dont commit the same mistake that happend to me.
I thought I had it undercontrol and failed missierably. Its like dabbling with dope if you ask me.

Just cut your losses and find some other chick. She is going to use you to go out and wine and dine her just for her own ego boost.

You know, part of me keeps saying the exact same thing. I'm freezing her out right now, but I feel like it's going to make the situation worse, unless I completely cut bait.

I'd take her invitations... Go for drinks, sushi, whatever...

And escalate like there is no boyfriend. Don't mention him.

See where you get. If she rebuffs you and she's firm about it, then stop wasting your time... Cause that's exactly what you'll be doing.

Freezing out does absolutely jack shit unless she's invested in you.

Stop playing the fucking games. Just escalate. See what happens... You're wasting time and mental energy on a nutjob...