What is that "I ♥ NY" typeface?

I've been looking into the history of Milton Glaser's classic "I [heart] NY" logo for a side project I'm doing. There are lots of stories out there, but none of them mention the name of the typeface that Glaser used.

My friend Ottilie teaches typography, so after a couple of hours of fruitless googling I turned to her. And it turns out that she doesn't know either:

Gosh, I know a great deal about Glaser (even met him in Aspen one June!!) and the story surrounding the logo, including his re-make "I Love NY More Than Ever." I can think of several of his typeface designs (Baby Teeth, Glaser Stencil, etc.); Push Pin Studio, etc. But I haven't the foggiest what typeface this is. He may even have (very likely) created the letters only.

He did that for New York magazine. As did Herb Lubalin originally for Avant Garde magazine. (Herb Lubalin originally only created the letters in the words, "Avant Garde." The complete typeface came some 10 years later.)

There is also a funny story about Glaser being told by some young upstart that HE couldn't use the design (when he designed the post-9/11 version). Glaser had to inform the bureaucratic minion that he was the guy who did the original logo, for free!!

So there we go... looks like it's bespoke type (and therefore not available on 1001freefonts.com)

Update: Suzanne writes "American Typewriter, or so says my font freak pal." Some further investigation reveals this Typophile thread where danlevenson says "The consensus seems to be that Glaser used American Typewriter Bold - a "no-brainer." But the version on Milton Glaser's web site... as well as every version I have ever seen, is slightly different. ITC American Typewriter has a lot more color than Glaser's version."