Your stamp is a type I, rather than a 1a. (Note the toga button and rope are weak on your stamp.)
Thus it is a genuine 409 or a 482 depending on presence or absence of a watermark, with Schermack type III vending perforations. And far more likely to be 482 due to the 1919 use, which I agree with, as you found out, this slogan was used only in December 1919, and almost exclusively in New York City. Here are a few full examples:
