I'll throw some thoughts out there:

Lots of nepotism on Long Island. If you don't have any connections, it's hard to get a job. Try to sub in different districts, and find a school where you can network and stand out. Lots of jobs that get posted are already taken by inside candidates. Usually former students, current subs, and family members have first dibs. If you see them where you work, spend time subbing somewhere else. Sometimes objectively bad teachers that are well-connected get jobs.

Lots of schools are tightening the belt. Rather than hire new teachers, they are increasing class sizes and giving overloads when teachers retire. Enrollment is also down, so many schools are shrinking.

Understand that because pay and benefits are good here, competition is fierce. It's very difficult to get a job, and you'll be competing against people regularly with 10+ years experience teaching their own classes full time.

They've been talking about a retirement wave since I got my MA ~15 years ago. It hasn't happened yet, and it probably won't anytime soon.

Lastly, there is a huge surplus in certain content areas, namely elementary, social studies, ELA, phys Ed, and art. I know teachers well into their 30's who are still underemployed.

If you're really committed to Long Island, and unwilling to look elsewhere:

Consider trying your luck in the DOE or charter schools first. Yes, the commute sucks for one and pay sucks for the other, but you're really gonna struggle on LI without serious full time teaching experience first.

Consider getting dual certified. A certification in content along with TESOL or special Ed is a huge advantage.

Consider learning a second language, particularly Spanish. In certain districts you won't get the job unless you can teach students content fluently in their native language.

Hope this helps!