Refinance and hold on it indefinitely.2.

Somewhere along the way I decided that I wanted/needed to be in a position where, if needed, I could drop everything for an indefinite period of time for a loved one.

If it is amortized over 30 years and the lender will let you keep it indefinitely then consider keeping that for longer.

Assuming that every year indefinitely the same return can be expected.  

I do not wish to live in NYC long-term or indefinitely.  

Only the 1031 indefinitely defers all tax and depreciation recapture and can be eliminated in your estate.  

But I think your reserves should take into account your financing situation, any upcoming bullet payments, overall monthly debt load and cash margin...I think I could cover the debt service on my properties indefinitely with my current reserves, and significantly declined rents of about 20%.

This means if it is a lease with an option and you're following your state guidelines so it is not considered a "sale", you can technically duplicate this process indefinitely. 

I have the option to either delay closing indefinitely until they make these changes, or it has been proposed to put a good chunk of money ($20,000) into an escrow account from  which I can draw to make the changes myself, after which the remainder will be returned to the seller. 

If the market cools you're going to own that thing indefinitely or take a loss on it.