Getting serious again for a moment... :P

I'm still wondering where the narrative of "Donkey Riding" as some celebration or parody or commentary or critique of donkey engines came from.

My first guess would be one of Hugill's writings, but it's not with the description of the song in SfSS, and I cannot remember where (other books of his), if anywhere, it might be.

Perhaps the idea came in some album liner notes?

I may be suffering from temporary blindness, but are there really any statements (i.e. aside from popular hearsay) that connect "Donkey Riding" with "donkey engine" at all?

I do see that a 1936 book called "Sing Together" (put together by Girl Scouts of America) offers "Donkey Riding"—evidently after the Oxford Song Book version—listed as a "Canadian sea song" and including the note, "Donkey, of course, refers to the donkey-engine." Of course. (?) Its seems a bunch of other mid-20th c. song books included "Donkey Riding," and they may have repeated the idea. The whole "children's song" dimension to the song developed.