I've been looking for this place for a while too. Here's a few more possibilities...mostly weak ones:

Alcazar Club, PO box 374, Biloxi, MS
A Taylor & Co customer or potential customer. "James E. Hertzog" is a name appearing in the Taylor & Co business contacts file. Have been looking for Shivel and Green in the census but no luck yet. There were some Shivels living in the area though.

Alcazar Club, Broadway Ave., Chicago,IL ca 1920s
owned by Al "gorilla" Weinshenker, one of the St. Valentines Day Massacre victims. Don't know what happened to the place after Weinshenker's death.

Alcazar Cigar Store, 414 Fulton St., Peoria, IL, ca1930s
William Urban & Frank Daugherty were the owners...no Shivel & Green

Alcazar Hotel, Chicago, ca 1940
Taylor & Co chips purchased by B. Shannahan in 1940

There's a Kentucky option I'm exploring too. Maybe more later.