I hear it as being played on a Bb Cajun accordion, in the second position, F. Most of the song alternates between the F chord and Bb, with some other interesting chords added in the chorus.
Maybe there's more than one version? The one I heard is defintely not in the key of C, and not on a triple row. The licks sound a lot like typical licks on the "pull", or second position.
I thought I was hearing some Allman Bros motifs in there!
I still think it is on the pull, not the push. On the triple row, you could play it on the outer row (the F row) on the pull (key of C). This is assuming an F/Bb/Eb triple row.
But, you kinda already said most of that. Don't mind me - I work in the Dept. of Redundancy Dept.