Not that I really want to shoot holes in my own theory, but I tried this on a 503 Rocketeer, rotated the bare shaft in the normal direction until the needle was down or going down and the slots on the shaft vertical. I reassembled hand wheel, lock washer, etc, and it's the opposite. The tang corresponding to the stop had to be down.
I then tried it on a recently acquired 15 clone, and, although the needle didn't go down as far as on the other Singers, it worked the same, meaning the tang corresponding to the stop was installed at the top.
My modified theory is that my original proposition is for black Singers.