I'm serious as a dead horse!

I think the engine connection is very plausible-sounding and elegant by itself, but there is a conspicuous lack of evidence.

If we could get a sense of when any of the stories about the shanty and donkey engines started, it might be a great example of how shanties have become mythologized.

The 1936 kids' song book I mentioned may have been among the earliest to interpret "donkey" as steam donkey. The book is not authoritative, which means the editor either made the leap without expertise, or got the idea from some still unidentified book written with expertise. I have only seen a snippet, but it's enough to suppose the 1936 version came from the 1927 Oxford Song Book, which makes no mention of the engine. I reason, tentatively, that the 1936 editor took the liberty of interpreting "donkey."

The fact that none of the sailor-based books to give the song (i.e. Oxford, Hugill, Harlow) mentions the engine suggests that either there is no engine connection or those writers were unaware of it if there was. Hugill would certainly have asked what "donkey" meant, and given the engine explanation if he'd got it. That was his style.

If we assume there was an engine connection, who were the people aware of it? The editor of a Girls Scouts songbook? Were there other old salts, participating in oral tradition and engaging with "new salts", that handed down this information? Or did some of the newer salts put it together on their own?

How far back was the explanation heard (about the engine inspiring the song) and from where?

I can't remember where I first heard it. It may have been on Mudcat. It's nagging me.