OK, here's an effort to advance some idea that's not a joke or pun :)

1. First, let's remember that there are not too many documented versions of this song in its "original" context. Among them are LA Smith's earliest print mention of 1881, with "ruler king," and Lydia Parrish's "rolling king." (Let us please not speculate anything based on the "Nancy Blair" revival version!) If there was any referential meaning to the phrase, then several if not all of the variations known to us were mondegreens/mis-hearings, either as passed on through tradition or as recorded by collectors. For the sake of argument, let's assume that there *is* something meaningful about the phrase, but let's not assume that any of the forms we known are necessarily original -- i.e. there is something to be found, but stay loose with its form.

2. I have reason to believe that "South Australia" derives in style and spirit from Southern U.S. popular/folk song style in the minstrel genre or in the shared vernacular song traditions of that area that are otherwise hard to separate. This belief is a major assumption in my hypothesis. However, I feel much less certain whether the "South Australia" represents a more or less unique creation on this *model* or whether it might have been a more specific parody or reworking of some yet-to-be-discovered song. To pursue this further, I am going to commit to the idea that it was a parody or that it re-used the basic structure of an existing song.

3. We know that chanties of this sort had highly variable (in many cases, completely un-fixed) solo verses, but that the choruses tended to remain constant. I have said before that the "identity" of a particular shanty lies in its chorus and not *necessarily* anything else. Of course, these choruses, too, were subject to variation but that was the result of oral transmission, not the result of a built in understanding that they should be changed. So they were fairly stable.

4. We also know that many chanties were adapted from songs that originated in non-maritime contexts. There is no reason to assume that "rolling king" has necessarily anything to do with a ship or a deep-water sailor's life/work. I think to do so gets us stuck. Moreover, if, as I am assuming for the sake of argument, "South Australia" was based in another song, then we should be open to seeking a meaning for "rolling king" that fits in non-deepwater contexts.

5. What might these contexts have been? What sort of song was the "original" -- the framework and chorus which was varied, with new context-specific solo verses, to form "South Australia"? I suggest this is where we should be thinking.

6. Along theses lines, I am thinking of the songs of the Black firemen on steamboats. Their worksongs were well known in the mid 19th century. They are songs in which the phrase "heave away" was actually used. Take the example from Allen's SLAVE SONGS (1867):

This is one of the Savannah firemen's songs of which Mr. Kane O'Donnel gave a graphic account in a letter to the Philadelphia Press. "Each company." be says, "has its own set of tunes, its own leader, and doubtless in the growth of time, necessity and invention, its own composer."

Heave away, heave away!
I'd rather court a yellow gal than work for Henry Clay.
Heave away, heave away!
Yellow gal, I want to go,
I'd rather court a yellow gal than work for Henry Clay.
Heave away, Yellow gal, I want to go!

With this I begin to speculate whether "rolling king"/"ruler king" could mean something in reference to riverboats. Isn't there a big wheel that "rolls"? Didn't these boats have names with "King" or "Queen" in them?

In the 1868 article on "Songs of the Slave" (McBride's Magazine, no. 2), there is a "steamboat song" with this text:

What boat is that my darling honey?
    Oh, oh ho, ho ay yah yah-ah!
She is the "River Ruler"; yes my honey!
    Ah a... yah a...ah!

So, "River Ruler" is the name of the boat. Ruler King? Rolling King?

Speculation, but an attempt to think outside the hull!