This strange-looking accordion was start of my interest in the uniform keyboard layout. In specific, here's the layout on the treble side -- the picture below matches the rightmost picture above:
The accordion is branded Robotti. Most likely that's not the manufacturer, though. There was an accordion school called the Robotti Accordion Academy (alternately Robotti Moser Studios) in New York City back in the 1940's. I found the following scans poking around the net (someone was selling this brochure on eBay):
In that era, it was common for schools to contract with an accordion manufacturer to produce instruments which were branded with the school's name. The instruments were sold to students at the school, which was a good deal for both student (who got a good accordion at a reduced rate) and the school (free advertising).
I believe that my accordion was manufactured by John Reuther. Under the grille is a handwritten note in pencil: "Pat. 2,203,393". This the patent number under which Reuther filed his claims for the 3-row uniform keyboard layout and action. Here are scans of that patent from the US Patent Office:
The mechanism depicted in the drawings matches the mechanism in my accordion. Pretty neat.
Hans Palm has an article by Reuther in a British magazine, wherein he describes the layout and its advantages. Here's a local copy of said article: