The 1929 recording by Angelas provides us the best source for this. The lockstep is evident only in the A part, with the B seemingly carried by the accordion. Clearly, Angelas has been playing for quite some time before the recording, he powers through the song with speed and embellishments. However, given that Dennis felt comfortable to play the tune again in the 70s demonstrates he was probably versed in it well enough to have lead the song back in the 20s. He wasn't solely capable of only playing second fiddle for this.
By the 1930s, string bands adopt the song and it remains mostly a fiddle tune until after the war.