Quitting IB Job Without Another Lined Up?

I'm a third year analyst at a top BB who just switched groups (previously in the tech group in SF, now in M&A in NYC). I've been on the desk for two months now and needless to say it's absolutely miserable. This group is widely regarded as one of the top on the Street, but it's been absolute hell. I switched over from the tech group after finishing up my two years (did not like the bay area) which is also a notoriously sweaty group and this makes my first two years seem like a walk in the park. In my first two years of banking, I probably worked 120 hour weeks once or twice. I think I've already logged 4 in my first two months of joining this group. Any given night, I usually have 4 different teams chasing me for work at 12:30am and am averaging like 3 hours of sleep during the week. I haven't had a day off in over 4 weeks and each Sunday has been a normal workday of ~10am to 1am. 

I don't think I can do this anymore. The work isn't rewarding, I feel like my learning has plateaued and there's literally 0 reason to stick with this as I have no plans to be in IB in the long run. Main reason I haven't left to the buyside yet is because I quickly realized I didn't want to be in the Bay Area for more than 2 years and wanted to focus on buyside roles in NYC so thought it'd be best to recruit out of NYC so that drove my switch (I also enjoy M&A as a product and that has always been my focus even in tech). There's a bunch of solid immediate start hires going on, but I legit have 0 time to recruit and the free time I do get for a few hours on Saturday, is usually spent clearing my mind out with friends. 

My question is this: how bad would it be to straight up quit my current job and purely focus on recruiting for near-term starts? I know the consensus is usually "take your foot off the gas at your current job, stop responding and focus on recruiting" but that's nearly impossible with a different VP calling me every 2 hours and the expectation to be in the office almost daily now. Being that I'm new to this group, either way I would use references from the tech group as I know they'll speak highly of me and I can just say "didn't feel comfortable giving this group as I haven't worked there long enough". Would the HHs or PE firms know I am currently unemployed if they do not contact my current group? I'm worried that me being without a job screams "this kid can't handle when things get tough" so I wouldn't want to outright say I quit. My plan would be to recruit like normal acting like I'm still on the desk and then hoping there's no way to actually check that I'm still there.

I'm at a breaking point after being up until 5am on a model and then waking up at 8:30am to 4 missed calls from my team asking if I've made the updates to the buyer log so any advice here would be greatly appreciated.