Chanteymen were varied in their repertoires, I see no reason to be "skeptical" of their verses or combinations of lyrics from different songs.

Ah, but it is not "chantymen" about which I am skeptical, it is about the published texts of many authors who either were not chantymen or who had ideas that things should be changed for publication, in accordance with either propriety, artistic aesthetics, or with what had come before in writing. I only mentioned being "skeptical" of Masefield. Just look at his version of "Lowlands" in the same volume, and you'll see that it's ridiculous -- he obviously made it up for publication. If he does that and he also is borrowing from other books, it casts doubt on *all* his verses, as far as I am concerned -- having been a sailor doesn't give him a free pass. Likewise, Hugill presents many verses from Masefield, presenting them as part of "variants." Hugill's clout as a chantyman compels us to consider them, but they aren't something chantymen are documented to have sung.

Luckily, by looking close at the source, we can get a pretty good idea which are chantyman's and which are writer's lyrics.

I can't imagine "Rio Grande" or any chantey retaining the same lyrics over time, that ain't natcheral.
Also a goal of the historical survey: to notice which versions are too similar to be naturally likely...thus suggesting a copycat writer.

I also would dispute that sailors would always have sung bawdy lyrics.
No one said that they did. There are plenty of accounts that say they didn't. But it was Harlow who emphasized how common dirty verses were on his voyages, and he admits to bowdlerizing them.