These are fine guns and I am happy to play.
Here is 634373 and an appropriate first-year box (but not original to the gun). Like Richard's, this one also shipped in June 1931, but I don't have the destination or exact date. Time to break out the letter request forms.
Here is my other K-22 OD, 646390, which shipped April 1934. I believe this is the lowest known serial number with the two-screw rear sight foot. (Two at the back, that is; we don't count the one at the front of the foot.)