We need a PICTURE of this critter. I've had a bunch of 37s, 37As, and 370s and none of them were as the OP describes. (My first gun was a 37, a .410 with 28" bbl. bought new in 1951 for $23.50; still have it, still hammers cottontails).
Nor do my references site any prototypes like that. Seeing is believing. And, like Fox Mulder, "I wanna believe!".