Re: "chant" vs. "chaunt."

The OED is sketchier on this than I'd like, but it appears that "chaunt" was simply a variant spelling of "chant" that arose in the 18th Century for no particular reason and faded away in the 19th.

Possibly the spelling was to emphasize the "ah" or even slightly "aw" quality of the vowel in cultured English; the alternative "aa" vowel (if you see what I'm saying), which is and was the usual thing in some parts of England and all of America, may have been thought low class by some.

As for the Gibb's creole "chaun" meaning "shan't," it suggests to me that in that part of the world "sh" was often pronounced "ch" rather than the other way round. The "other way round" is what we're looking for.