My rescue pooch is sadly approaching end of life, as best I can tell. So, I'll be going through this process again some day in the not to distant future.

I'm not in New York, but I will say that when I was last looking to adopt, there were aspects of it that were definitely off putting and demoralizing. Some of the rescues had ridiculous requirements that made me wonder if they were actually trying to place their dogs in a home. One of the most egregious that I semi-recall: It was a breed-specific rescue (ex: Norwich terrier), but most of the dogs they were trying to adopt out were mixes. They required you to have owned that breed of dog before. You had to be in a long term relationship (i.e. no single people). You had to agree to let them make a home inspection every 6 months. They had to be added to the list of approved contacts at the pet's vet. They could take the dog back at any time and for any reason. Etc.