I agree with your reasoning, Lighter.

Yet, some possible arguments against:

1. If the song originates in the stage/commercial sphere, I wouldn't rule out the first-person-singular voice.

2. Some of the "post-romantic" tone could be later accretion as the song developed through later periods. The chorus of "WE'RE bound for Valparaiso" could be an older bit, with new balladry spliced in as the solos.

3. I'm somewhat put off by the prospect that the 1868 writer would include a straight up ballad, no chorus, among the shanties. Even while "Paddy Get Back" is not the model chanty, and (by rough count) as many or more sources say it wasn't a work song, it does "work" as a capstan work song. I might be giving the writer too much credit, but I lean towards suspecting they would have distinguished such a song as "Rounding the Horn" rather than lumping it with the other repertoire.