An Ngram of the term shows its birth as a "stock phrase" only dates back to the 1960s, but the words are found in print a century earlier and the first examples of the phrase being used to mean motivating, inspiring, or enabling forces or factors go back to the 1930s. I'll give you one example of each.
I found creative juices in print back to this 1846 translation (p. 182, scroll down) of Kalevala, a Finnish epic poem that recounts a mythical story of the cursed birth of steel:
I don't think this reference is incidental. The same section of this poem, with the same translation, was reprinted several times in the writings of Lafcadio Hearn at the turn of the century and as late as 1922. While not the figurative use of the phrase we have today, I think there's a good chance its occurrence in his writings led to its familiarity and adaptation in the 1930s.
The first use of it I could find in print with its modern connotation was from this 1936 article in The Delineator:
[...] and played and replayed and recorded and wrote down their early songs.
Their creative juices dried up. Only a
few of the original players stuck by
their guns, among them notably the men
mentioned in this article. They
continued, in honky-tonks, dives and
dance halls, to play as they felt and
feel as they played.
I wasn't able to get a more complete quote because of the limitations of Google's Snippet view, but it's clear the article is referring to the figurative creative juices of musicians.
One later 1930s reference of note is found in the intro to the 1939 screenplay of Margaret Mitchell's Gone with the Wind.
Umpteenth comes from umpty, meaning an indefinite number. Etymology Online says "umpty" is derived from "Morse code slang for "dash," influenced by association with numerals such as twenty, thirty, etc."
And I think the "teenth" insert is to make the "th" easier to pronounce for the ordinal formation, but it might be also to add emphasis by way of lengthening the word. Also, it might be because of the teen/ten connection I mentioned in my comment above: an indefinite number of tens.
And this source suggests that Morse code slang word "ump" is imitative in origin, so I gather that means that that's what a dash sounds like in Morse code.
It occurred to me that this means something like _th times, then, or the equivalent of nth times (to the nth degree?)—although a single dash is Morse code for T.
Best Answer
Yep first showed up in the late 19th century US and spread from there. The Oxford English Dictionary ("yep, adv. and n.") speculates that it comes from "Alteration of yes adv., with an apparently arbitrary element." It's rather like "nope" in that way - the /p/ sound is an arbitrary ending that probably manifested first in oral speech as a quick reply. Its first published uses tend to be in quoted speech:
Yeppers is a diminutive or emphatic form of yep formed with the colloquial suffix -ers. (See preggers.) It isn't usually included in dictionaries, and in corpus searches from the early 20th century the overwhelming result is a misscan or misprint of peppers.
An early usage emerges in 1929, though it appears to be a nonce formation that uses -er to refer to people who say yep (from The Literary Digest, Volume 99, 1928, p. 29):
As an affirmative, the earliest example I can find is from the magazine Descant (1987), p. 13:
The form may go further back in time; again, this is most common in oral speech or quoted speech, so there most likely won't be one traceable point of origin.