Currently a senior analyst at a BB - accepted my MF/UMM offer but regret it - what do I do now?

This may be unpopular advice that runs counter to the grain. I think it's possible to walk out of something and maintain your reputation by acting in a high-character way.

Call the headhunter or the recruiting lead at the firm you previously committed to. Explain that you've reflected on it for months, spoken at length with the core group of people you respect and look for advice from, and turned it over and over in your head. Your honest conclusion is that the role isn't right for you. It's not a them-versus-another type of situation. It's you re-evaluating your life and goals and having an honest conversation with yourself. 

It's kind of hard to knock that. Sure, people can get angry. This industry is definitely full of immature people who have a low level of self-awareness or perspective. Don't be surprised if one or more of the people involved in the process take it negatively, but persevere.

Don't get off the call without pushing past any negativity to reiterate that you were very committed when you signed, that everything you said in your process was sincere, that the opportunity to meet, speak with, and learn from them during the interview process is something you're grateful for, and that you are grateful for the opportunity.

Frame it as you feeling a burden of responsibility to deliver your best work, and after reflection, a sense of duty to tell them you can't be that for them. 

Stepping past everything I just said, you can go a different route (or combine with everything I just said) and be a bit disingenuous. The pandemic offers the perfect air cover for anything you want to say. You have a family development that's changing your life. You need to relocate for some sort of personal reason. You are developing a health concern. There is just about nothing you can't say as evidence for why you aren't prepared to take that role. 

The downside of this alternative path is that if or when people at that firm see your LinkedIn at a different firm in the future, they'll read it as what it was: a smokescreen.

I think honesty is not amiss here. Very early in my career (picking between internships) I wish I had practiced it, I didn't and a number of people rightfully looked at me unfavorably. I have practiced this in a lot of different scenarios. I have chosen who wins the auction for an asset of mine. I have returned or declined eight (in one case, nine) figure LP checks. I have fired senior investment professionals. I have replaced management in portfolio companies.

I find that sitting down and explaining where I'm coming from, why this decision matters to me, how I got to where I got, and what I think of the person regardless of the decision I have landed on makes it possible to deliver uncomfortable or unhappy news without severing a relationship completely. People have called me months or years later to thank me for how I acted in that moment, or skip mentioning it explicitly but through their behavior show that they're still a fan of me (showing me another deal, trying to buy something else off of me, whatever).

You're at a crossroads. It sounds like you recognize it. Leaving banking is one of two guaranteed shots to be viewed as a blank sheet of paper. The second is business school, and that's unfortunately to a lesser extent because it's colored by your pre-MBA experience.

Put plainly, there's a realm of firms that won't want to hire you or will screen you way harder once you have buy-side experience relative to having none and interviewing for that first investing role. It's hard enough to train people well. It's harder to un-train them, and for better or worse, many people prefer a blank vessel to one with habits that may need to be unwound to fit in at their shop.

Good luck.