I would say this is endless summer. At least it is in Ohio, not sure about New York City. This is one thing you often overlook by focusing on the anomalous past warm years, there were a lot of historic years that were VERY cold.
Looking at Cleveland, the first two weeks of October is running warmer than several historic Junes and even some of the coldest Augusts. Nobody would say June or August aren't summer months, just because they are colder than average. So if those months were colder than this October, and yet still considered to be summer, I would say you must accept that it is still summer.
The mean high temperature for October so far is 72.7F.
We can see there were 18 historic Junes with mean high temperatures for the month at or below that temperature, most recently in 1972.
And, for August, we can find one cooler year (1927) and one just 0.1F warmer than this October to date (1915). Nobody would say August 1927 wasn't a summer month.