Since you are planning on installing a new floor over an already existing one, then engineered flooring is indeed, a wise choice. I'm crossing my fingers that you will be able to click-attach it throughout the entire floor, but if the surface you are laying it on is a bit tricky, you might have to use secret nails. And since there's an existing damaged floor underneath, if you were to ever remove/replace both, you would be creating yourself some unnecessary work.
Before my wife and I moved from London to NY, we had an engineered flooring from Kahrs in our house. We bought it from a local company, and we were quite satisfied with it. Furthermore, they are equipped, so to speak, with a hard to scratch top layer, that makes them ten times harder to scratch, compared to other engineered floors. I am a bit lost as to where you would be able to find it in New York. I wish you good luck in your search though, because it Is definitely worth it.