Buying this house took pretty much all my funds.

You can use hard money and start buying properties then refi out of it.

I am interested in buying a property near NYC for STR.

I am new to the game, but do homebuilders consider buying distressed properties, tearing down and rebuilding?

I would not buy a property here unless it had solid cash flow.

My loan officer is saying no, but the literature I'm seeing says up to 12 months delayed occupancy is allowed for special circumstances.

You've been living there for 15 years, and some new rich landlord buys the place and starts raising rents.You need to go on a per unit basis, and address any issues that need repair.

Some key factors, or questions I often get from the investors I work with on the buy side for STRs, that you can focus on in your listing, are as follows. 

Investment Info:Single-family residence buy & hold investment in Wilmington.

Quote from @Michael Daniel: It's very important to know what you are buying, which includes confirming the presence of a written lease and what the terms may be.Your offer to purchase should include a requirement that the Seller provide all documentation and agree to sign an estoppel certificate (also called an estoppel form or agreement).