No music... yet. Our lyrical world is sure getting smaller though. Mitford's ultimate source for Mike Fink was Judge James Hall's The Western Souvenir for 1829 (Cincinnati.) Haven't located the original but, The Last of the Boatmen chapter with Shawneetown and beach oar (with an “a”) appears in: The Critic: A Weekly Review of Literature, Fine Arts, and the Drama, 10 January 1829:

The literary contents of this, as of the other Annuals, are furnished by different writers, among whom the editor has performed the largest share. The prose portion possesses greater merit than the poetical. We copy the opening lines, by James Hall, which are a favorable sample of the latter; and the sketch, entitled, The Last of the Boatmen, which bears the signature N. is perhaps as interesting as any prose selection which we could make….

N=Morgan Neville (1783-1839) per Beginnings of Literary Culture in the Ohio Valley: Historical and Biographical Sketches, Venable, 1891.