I have a personal favorite theory that, as far as I know, has never been published. I think "the whole nine yards" derives from an older expression "the whole megillah," which was (and occasionally still is) used in exactly the same way as "the whole nine yards."

The origin of "the whole megillah" is a lot easier to explain. "Megillah" is the Hebrew and Yiddish word for "scroll" and most often it specifically means the Book of Esther, which is read aloud in its entirety on the Jewish holiday of Purim.

It's a long reading, and it's natural, if you want to emphasize its length, to describe a scroll in terms of its physical length, e.g. "nine yards."

I have no idea how long a scroll really is, but even if "nine yards" is an exaggeration, it doesn't disprove the theory. Hyperbole is common in folklore.