My guess is the matter will rest on what the grand jury defines as "reasonably believes"worth reading the laws of NY regarding physical and lethal force!
Article 35 NY Penal Law - Defense of Justification | NY Laws
Justifiable use of physical force, conduct which would otherwise constitute an offense is justifiable and not criminal whenypdcrime.com
he or she reasonably believes such to be necessary to defend himself, herself or a third person from what he or she reasonably believes to be the use or imminent use of unlawful physical force
In the end, I dont think New Yorkers are willing to stretch "reasonably believes" to using lethal force against annoying homeless people who are A, unarmed and B. did not actually attack anybody.
I had a homeless, long term crack addict (judging by facial expression and body movements), approach me while placing luggage hotel in Compton, CA. She then started screaming profanities- some creative, most not. Trying to ignore her, I went back to the hotel lobby. She followed me into the lobby where my three young children were- still screaming profanities.
I have a feeling that if I strangled her to death based on the premise that she might have intended to harm one of my children, the jury was not going to buy it as being truly needed. Hotel staff later told me that she was a "regular" in the area and had never attacked anybody.