Apologies. There's a nine-stanza printing of "Tommy Linn" [sic] in "The Distracted Sailor's Garland" of ca1770. Will post shortly.

Nineteenth century British quotations of the song seem to hark back to this version.

I agree that "Tom Boleyn" (Or "Tambolin" or "Tom a'Linn," etc.) is most likely to have been the song mentioned in "The Complaynt."