Right, John, back to the fray after a couple of hours spent with Bronson...

"On the banks of the old Tennessee"! Where did that come from?"

This looks like a regional amendment to "the banks of Italy" found in all of Child's Scots texts. That there are no such banks, or comparable locations, in the older English texts (Child 243 A & B) suggests that De Marsan is not derived directly from the latter.

Looking through all of Bronson's North American copies, this is one of the features susceptible more than any other to variation. The promised banks may be those of 'Sweet liberty'. 'Dundee', 'the low country', or the 'salt salt sea', as well as many more or less nonsensical substitutions like 'sweet Marie', 'sweet Vallee', 'Aloe Dee', 'Daiee', 'Otie', 'Murree' and 'Lacolee'. The 'Banks of Claudy', mentioned in Mrs. Sullivan's version from VT, were presumably imported from another song. The most common is the 'Banks of Sweet Willie', with over twenty examples. I counted just four 'Banks of Tennessee', which suggests that the influence of the De Marsan broadside was limited or distant in time, but there are at least a dozen 'Banks of Italy', harking back to early 19th century Scots oral tradition.

Other features of the ballad very common in North American variants but absent from de Marsan are the 'Hills of Heaven / Hell' (at least 32 examples), which are first sighted in the version from Scott's 'Minstrelsy' (Child F), and the scene where the eloping woman dresses herself in finery, frequently being seen to "shine like glittering gold", which isn't an exact match for any of the Scots copies, but recalls the 'glamour' cast over her in Child E, v8 (Motherwell's MS).

On the other hand the incremental repetitions of De Marsan are matched in over seventy different American versions, usually as:
'They had not been on the sea two (three) weeks,
I'm sure it was not three (four)',
which is slightly different from the De Marsan formulation.

Last verses following De Marsan's, along the lines of: 'A curse be on the sea-faring men' (the 'sea-going train' in two versions!), are reasonably common but by no means universal.

Other American variants include archaisms that may go back to older British tradition, such as sailing for two leagues, rather than weeks (Bronson #18), the 'dark and dreary eye' in Bronson #102 (recalling 'dark, dark grew his eerie looks' in Child G), and the name 'George Alliss' (suggestive of 'James Harris?') in Bronson #141 - the aforementioned version from Springfield VT.

All of which supports the idea that the De Marsan broadside, although it may have contributed to the ballad's popularity in America, was not the only means by which it was spread. There may have been other broadsides, of course, but some of those variations look a lot more like the result of oral transmission over generations. In that context, it's interesting that Lena Bourne Fish's father was a Scot - and thanks for posting her text.

"Is Heylin's work on line by any chance?"

Not that I know of.