is there anything in the NYS law that would prevent me from doing what I describe, proving that zoning / permits / licenses are taken care of?
I believe I answered that question. The answer is yes the government on one level or another can scuttle your plan to operate a week-stay vacation hotel out of your residential property(s). How bulletproof their case would be depends more facts than you have given, or should give on a public forum for a prospective venture. Your ability to secure those permits and licenses and zoning approvals are the hard part, so assuming that as a given is ridiculous. An answered based on ridiculous assumptions is useless.
Personally, I am of the opinion that what you are proposing means you are becoming an innkeeper, and will face more regulation than being a landlord renting long term. You might have to worry about the occupancy tax then, you don't want to hear about that, even thought the tax law basically proves that what you are doing is running a hotel....
http://www.tax.ny.gov/pdf/publications/sales/pub848.pdf
I'm sorry your question doesn't have an easy, and I think you were well aware of that given the press on the issue.
If you plan to become a landlord or engage in thew letting of your property, here is a hint - Every savy landlord has a lawyer review their business plan and legal documents. That smart landlord keeps that relationship with that lawyer going in case of issue with tenants.
Good luck on your property venture. I'm sure you can see that it is potentially lucrative and that is why their is scrutiny by the authorities.