Let’s be honest, you don’t need a government and a school district for accountability. Those people are the reason most of us homeschool. I don’t want them to know we exist.
We moved from Michigan (total freedom) to Maryland (”accountability”)
We searched until we found an umbrella school that is very low key and non-intrusive.
We also don’t take part in home-school co-ops as we believe them to be a crutch. Our kids are not brainiacs, well, one is and he’s studying aerospace engineering, the rest are self-supporting and good citizens, so the approach worked.
Honestly, don’t think that you need someone from the state judging your every move.
They didn’t judge whether we were doing well enough or not.
It isn’t that you are asking them permission. You are TELLING them what you are doing and the only thing they can tell you is if your curriculum does not meet NYS criteria somewhere, but they cannot tell you what to use.