The other thing I'm questioning is the originality of the tone control......first, why would you need one on a marching drum, and second, it sure looks conn-era Leedy (although conn era L&L was similar too) to me....
I wondered about why a marching snare would need an internal dampner as well.
I don't have much experience with marching drums from the calfskin era, but tone controls were common on marching snares from the late 1950s through at least the 1970s. You'll see the knob just above the badge on most WFL or Ludwig drums from that era. Rogers drums had 'em, too.
Mylar marching snare heads like the ol' Ludwig Silver Dot had a tendency to ring like crazy and the tone control was useful to tame that ringing.