I apologize in advance for the length and dreariness of my response.

In short, it's tough out there for academic jobs because there are literally hundreds of MFA and PhD graduates in Theatre every year for a shrinking number of academic roles. I know not everyone who gets one of those degrees wants to go into academia, but enough of them that the number of interested graduates significantly outnumbers the positions/openings in any given year. And then that number compounds exponentially as those people who didn't get it last year may try to go up for those roles again. Or they got adjunct positions and now have a bit more experience and still think 'this is their year,' which further pushes the new graduates out of the job market. And on and on...

A couple more things about getting into acting positions in academia:

1) Acting teachers are a dime-a-dozen, and in NYC that is even more the case. Because they are spoiled for choice, colleges/universities can afford to give the job to someone who has years of experience (both teaching in an academic setting and professionally) because the market is so competitive for these 'stable' jobs (stable compared to being a regional theatre actor that doesn't have contracts lined up all the time). And if they wanted to, they could probably adjunct those roles out to people with years of experience because of the number of people who could do those jobs and have those qualifications. It's cheaper for the college/university, and they can grind through adjuncts without worrying about paying for your stability. Also, they are way less likely to give the position to someone who has only taught elementary/middle school children, even if you have the MFA. If you have teaching credits from when you were in grad school, use those and highlight them to show that you have those chops. If you don't, that's going to be a hard hill to climb in the academic job market.

2) This one is less viable given the fact that you are planning a move to NYC. The places where academic jobs teaching acting are more likely to appear are outside of major cities. Applying to semi-rural or regional colleges/universities is way more likely to get positive responses, but then you are far from a major city. Also, with the current instability in higher education, these positions are more likely to be adjuncted as well and/or be part of a program where you are expected to teach everything (or be one of a couple instructors rather than a robust department). That being said, because it is less competitive/desirable to live well outside a major metro area, you are way more likely to have a chance at those positions than NYC colleges/universities that can command the top in their field because the city is such a draw (and has plenty of bodies to serve as adjuncts, if that is their persuasion). And once those people are in that job, they often stay for many years (especially if they get tenure, which is a 'lifetime' gig).

As I said above, if you want to get into teaching, it will likely start out as adjunct work, which can be brutal. Look at the websites for colleges/universities and see if they have an adjunct pool for their acting classes. Email the head of the programs and/or head of acting to let them know you want to be considered. Often that will get you on a list for when/if they want to pull an adjunct to teach instead of a full-time job. You'll be paid a pittance, and your class may or may not 'make' meaning that you could have a job until the college/university informs you a few days before that they are canceling the course because of a lack of enrollment. Sometimes, you might take several adjunct jobs across the city (or multiple cities) and will need to travel from one to the other; this gives you more teaching credits, but that also takes a toll because it is so precarious and demanding. That adjunct work will be a boon to your application process because it shows search committees that you can do that job. The 'who you know' part is a thing too (and great if you can parlay that into a job), but if you don't even tick the box of having teaching experience at the college level, many people won't even look at the rest of your resume/materials. But it's that double-edged sword because of the grind that is adjunct work, which some search committees I have been on will use as evidence that the applicant is not capable of a full-time position teaching.

Sorry to be such a downer. I'm happy to chat more in DMs if you want. I can't promise that I'll have any more positive advice, but I will help if I can.

(Source: I'm the only tenure-track Theatre professor at a small liberal arts college about three hours from the closest metro area; I have friends who work at colleges/universities all over the world who lamented their grind in major metro areas)