Maybe it’s just me (and Patch), but my hunch is that “the whole six yards [of it]” actually does have something to do with telling a complete story or giving a detailed report. And, by implication, going all the way in delivering the story or report (so maybe we are of a similar mind, Irishman).
Compare these forms:
[1964] “'Give ‘em the whole nine yards’ is an item-by-item report on any project.”
[1921] “The Whole Six Yards of It,” used as the headline of an inning-by-inning report on a baseball game.
[1916] “Well, Mr. Editor we must take our hat off to you. In your last week’s editorial you sure did give them the whole six yards and it did suit us to a T.Y.”
[1912] “As we have been gone for a few days and failed to get all the news for this issue we will give you the whole six yards in our next.”
[1912] “But there is one thing sure, we dems would never have known that there was such crookedness in the Republican party if Ted and Taft had not got crossed at each other. Just wait boys until the fix gets to a fever heat and they will tell the whole six yards.”
For me, the 1964 and 1921 usages give the impression of a detailed listing of factors or datapoints. A 1962 sighting of “all nine yards of goodies” (features on a new car) has a similar feel: it conveys an itemization or, as Doug Wilson has pointed out, a listing such as you’d find on a car window sticker.
Note 1964’s “give 'em,” 1916’s “give them,” and 1912’s “give you.” And note 1912’s “will tell.” “Tell” strengthens “give” in the sense of sharing/delivering something orally or in writing. (And note that there’s no “go” or “went” here.) If you’ve been of the WWII ammo-belt theory camp, it’s easy to see “give 'em the whole nine yards” as suggesting the delivering of bullets. I think, though, that the original sense of “give” is more subtle, conveying sharing (information).
My gut tells me that “yards” is a way of suggesting a (metaphorical) length of information delivered orally or in writing. (We have plenty of examples from the period where folks used “yards” in just this way.) And “six” because “six yards” implies further length, thoroughness. Perhaps folks were using other numbers before we eventually arrived at nine. But I do think that these early uses suggest that the idiom may have started as a means of signalling that all the details of a story (and similar) were, are, and will be given.