Holy Cow! You really did some research on it. I wonder if it would be worth writing the Singer Company to see if they could shed some light. I know that the Singer Featherweights have two badge numbers. One visible and one hidden under the column of the machine. I had hoped that maybe this machine had something similar.
I think I will try writing Singer and see if they can help with this mystery. I snagged this machine on eBay for $105. I used esnipe to get it to. I wondered if I had paid too much but given the condition of the machine, I have no regrets.
Gail