Lars, I agree with much of what you said, though I wouldn't (yet) go so far as to say the regt. was a hoax. I also looked at the company commanders and none seemd to have been in previous Indian units, as would usually be the case. But the papers of Jefferson Davis contain a letter from Indian leaders requesting Hunter as colonel, so there must have been a regt. of some sort and he must have been known to them. I suspect Hunter knew either David Hubbard or S. S. Scott, the Confederate Indian commissioners, and may have been recommended by them to the Choctaws and Chickasaws.
From what I have found out about Hunter, he was a fairly wealthy and well connected person, NOT a likely candidate to have committed such a fraud.