Welcome, Atlanta!
You're right: the Mafia's probable first foothold in America was in New Orleans through the Matrangas and their associates, etc. Later, Carlos Marcello in New Orleans and Santos Trafficante in Tampa pressed the cause forward. They may have had something to do with distributing moonshine, but I doubt they were involved in distilling it. Their greatest interests were gambling and drugs. Hot Springs, Arkansas, had connections to New Orleans, Tampa and Chicago, and at one time, Owney Madden, a big-time NYC Prohibition-era bootlegger and gangster, had a piece of the action.
Ony Virginia Hill (her full name) was from rural Alabama. Although she was primarily known as Benny Siegel's mistress, she in fact spent much more time, in total, with the Chicago "outfit" through her connection to Joe Epstein, second-in-command to Jake (Greasy Thumb) Guzik, who was Capone's second-in-command, and who ran the Outfit with Frank (the Enforcer) Nitti while Capone was in Alcatraz.