Thanks for all this information. I've been collecting info for twelve years about eephing, and the result is an article about to come out in American Music (academic journal), but until today I never thought to check the Mudcat Cafe site (I feel so stupid -- often!) and never noticed about the song Fats Waller recorded until I heard it on a CD a few days ago. Thanks so much for the info on that song. The article is in press, I think, so I don't think I can add a citation to this great thread.

In brief: The term "eeph" and "eephing" seems to first turn up in relation to a performance team of the 1890s, Williamson and Stone. Stone (the brother of star Fred Stone) died young; Williamson only revived his eephing briefly in 1918. But phrases relating to it, including the "gimme a piece of pie" reference, turn up in dribs and drabs through the decades. And what Jimmy Riddle calls "hoodling" also appears briefly here and there, including in the Cliff Edwards work mentioned in this string, and the "Swamp Root" recording you mention above, but also in a (very) few other places.