I did a little more reading - I highly recommend Bob Carlin's excellent book, Regal Musical Instruments, 1895-1955.
Harmony and Regal were two of the three BIG Chicago-based musical instrument companies in the 20th century (Lyon & Healy, originator of the Washburn brand, was the third).
Regal started in Indianapolis, briefly licensed their name to L&H, but by 1908 were established as an independent musical instrument manufacturer in Chicago. By the 1930's they were one of the biggest musical instrument companies in the world. They produced guitars, mandolins, ukes, banjos and other stringed instruments, as well as producing resonator instruments for both National and Dobro. Regal closed shop in the mid-1950's and sold the name; Fender was using Regal on lower-end acoustic guitars and folk instruments in the mid-1960's.
Harmony was founded in the 1890's, and bought by Sears, Roebuck & Co. in 1916 - back in the days when there was a Sears mail-order catalog in every home in America. The connection to Sears made Harmony a sales juggernaut. During the Great Depression Harmony bought brand names from failing companies (such as Stella, from Oscar Schmidt), and produced instruments bearing these names as well as their own. Just before World War II, a group of employee investors bought Harmony from Sears. In the 1950's, fueled by postwar prosperity and the rise of Rock and Roll, Harmony got even bigger, peaking in the mid-1960's. Harmony sold instruments under a variety of brand names, including contract jobs for stores and catalog companies (e.g., they had been producing, and continued to produce Silvertone instruments for Sears ever since the buyout). In the end Harmony was undercut by cheap Asian imports, and closed shop in the mid-1970's.
SO...given that the age of this uke (mid-1960's) coincides with Harmony's peak production, and that Regal was an old Chicago brand, and that Fender was selling Regal-branded instruments before Asian imports really took off, and that it has identical details to Harmony produced ukes of that time (I've seen ukes branded as Harmony, Silvertone, and Airline, all identical to this one save for the name on the headstock) - I'm confident that this is of Harmony manufacture in Chicago.
I have an earlier (mid-1950's) Silvertone of this design. It is the loudest and punchiest uke I own, despite it having a cracked soundboard!