Good point, but I honestly doubt whether "IWMES" was ever used to refer to the Berner Street club. "Eye Double-You Em Ee Ess" doesn't exactly trip off the tongue. "Hey, Hymie! Do you fancy comin' down the Eye Double-Yew Em Ee Ess tonight for a sing-song?"
Nice one That said, YMCA has fewer syllables, and those it has trip off the tongue a little more easily.
On another tack, whilst we love our acronyms these days - to the point of obsession - I'm not so sure that they did back then, at least not to the same degree. To my mind it would more likely have been referred to as "the Berner St club", "the institute", or just "the club" to those in the know. Or, possibly - given the lingua franca of the clientèle - a Yiddish equivalent.