I don't have my literature on that handy, but I do remember that the leaf spring production ended at least a decade earlier than the 1920 date you cite.  I believe it was closer to 1906 or '08.  One problem with the 'wals is that when a receiver gets separated from its trigger tang, the serial number goes with it. 

You can look at the top tang and see how the sear spring is mounted (screw from bottom or top, all the way through, etc. and whether the Winchester roll stamp appears on it...that will help somebody who has the right knowledge identify the general age, but of course not the actual SN.  You cn also look at the configuration of the frame (thin side or thick side, octagon or round top, groove or no groove on top, etc to get further hints of age.

Sorry to not be more helpful, 
Froggie

I have a high wall 26" 32-40 with a straight grip that has no serial number.  The tang certainly looks like it has always lived on the rifle even through a magnifying glass.  I suspicion that at least some of these rifles with no serial number were lunch box guns but how would you ever know.
Phil