I would guess that Dana knew the poem, Neptune's Raging Fury, since it has gone through many printings between the 1600s and c. 1840, was known to Pepys and appeared in collections of the Roxburghe Ballads (online, google books).
It apparently started life as "Countriemen of England" and is known by 1635.
None of that, of course, gives any indication of it evolving into a chantey.
The other two also would have been known to Dana as songs but perhaps not as chanteys.

This is probably repetition of previous posts, but there is now a lot to read through.