I am just about in complete agreement with your summary, Gibb, with a reservation on the linguistic side. Corn and corner are far too close to determine which one would lead to the other. One has only to emphasize the 'n' on corn a little too much, as can happen when singing, and you have corner. Alternatively word endings can drop very easily in slang lingo (Mas' Jones = Master Jones). The only thing I can add is, to me 'round the corner Sally' rolls off the tongue marginally better, but that doesn't help at all in determining which might have come first. A lingiuistics expert would have plenty to say on this. The strong 'S' on Sally diminishes the 'er' sound on corner to the extent that there is very little difference between the two phrases. Try it. However, if you miss off the Sally, the 'er' becomes much more emphasised. Well, in my Yorkshire accent it does.

Looking back through the thread we have 'Round the corner Sally' appearing in a minstrel song in 1843. The most likely source of minstrel song material is African American. If we assume 'corner' was being used by the slaves then this means they were using both 'corn' and 'corner' and the change happened there, or at least that both were in use on the American mainland before transferring to shipboard use. Or not!