Rain - I've slipped up. My 15K treadle is 1945 not 1940 (I have another Singer machine that is 1940) and it has the same stitch length knob, so I'm not surprised to see that a machine from only five years later has the same knob.
Thayer - My bobbin is like the 15K80 shown above.
Jljack - Kilbowie did not switch over to arms during the war but carried on with sewing machines. Some models had plain or black faceplates during the war.