The current state of the art in finding it in print or spoken word is from 1954, the movie Dragnet. The finder suggested that since Jack Webb, who helped to write the script, was a jazz buff, married to singer Julie London, it might pay to search out a connection.
The timing of the Dragnet episode and Mead’s connection to showbiz may indicate that the phrase in various forms was a current vogue word or expression of the day.
Underlying my silliness is the observation that we also have:
the whole nine yards
the whole shooting match
the whole ball of wax
the whole shebang
the whole magilla
none of which make particular sense. Quinion on “the whole ball of wax”, in which he mentions the Mexican food item in passing:
He cites wax balls from 1882. Perhaps this whole family of expressions derives from a little game whereby “the whole {whatever}” expressions were constructed, with {whatever} being some semi-random word that the perpetrator thought sounded amusing in context. Kind of like the “bee’s knees” formula which produced all sorts of silly “the {animal}'s {unlikely attribute}” usages in the 1920s, most of which died out pretty quickly.
ETA:
Exapno snuck in with the same reference while I was typing.
I’m afriad we’re never going to get the whole dope.
Yeah, I noticed the misspelling afterwards, when I glanced over the Quinion article again, and let it stand. It’s the way a lot of people hear it and spell it anyway, as a quick google will illustrate.