I looked into something similar in Maine at one point, though without state solar the money at play wasn't as much.
What I found, at that time, was there was a state class to take, a code of conduct, you HAD to be listed on their database with contact info (meaning people would be calling you as they would a contractor), and I believe there were a couple other things I am forgetting.
Here is what you would need in your state:
https://nystatewidecmp.programprocessing.com/programapplication/?ft=822091043BBC4F09A7D5F7DB2C9CF255The big ones that stand out to me is that you will need a certificate of insurance, which means you will need commercial insurance and the following training:
- U.S. Environmental Protection Agency Section 608 Technician Certification;
Certificate of ASHP Manufacturer-sponsored installation training; and
Certificate of ASHP Manufacturer-sponsored sizing/design training
There are members here who have done heat pumps w/o 608, legally I would not recommend that (MrCools with the pre-charged line sets might be their own beast). As for the other two, I do not think they make sense for a one off installation.
Also note you have to have an agreement with the utility company, which seems to be pretty similar b/t the companies. That requires the installation to meet incentive application requirements, I would suggest finding out if MrCool even qualifies before thinking any further.
For more details you can read section for of the manual, starting on page 61:
https://saveenergy.ny.gov/NYScleanheat/assets/pdf/NYS-Clean-Heat-Program-Manual.pdf.
4,400 on a 5,000 installation sounds like a lot. I tried to look up the specifics but based on what I found (
https://www.nyserda.ny.gov/ny/sun-pumped/Heat-Pump-Incentives) air source is by only some utilities, so I cannot dig further. In our state it billed as up to X,XXX where it is either a percent up to X,XXX of a flat for the 1st, 2nd ... units totaling X,XXX.