Some day when you've nothing to do but risk breaking an old screw, if you take the barrel off see what might be stamped underneath. Like, the barrel maker's name. Which still does not identify it but would be one more clue.
Remington was the most prolific barrel maker, but also NE of Ithaca, NY were Lull & Losey, in Pittsburgh Postly, Nelson & Co, and in Worcester, Massachusetts Hitchcock & Muzzy, later Muzzy & Co. The barrel may or may not be stamped CAST STEEL, which is more or less similar to a modern plain carbon steel like 1035 or 1040