Many thanks for uploading the Bargy "Sweet And Tender" and Banta's "Upright And Grand." You're right that I missed those two! The Banta piece is in a folio which I'd forgotten about, and on the Bargy for some reason my copy was not in the folder (hopefully not lost!) Good to fill in as many gaps as possible!!
One quick note on the Bargy interview upload - it seems that for some reason only the first two pages will open with Acrobat Reader, and the other two won't. I have this article from "The Rag Times" too (can't find it of course!) but I wanted to bring that to your attention.
You have put together an excellent collection of key audio recordings dealing with Charley Straight and Roy Bargy! The Victor record of "Ten Little Fingers and Ten Little Toes" is to my knowledge the only "live" recording of Straight & Bargy together, although they made dozens of duets on Imperial rolls. If only the duet rolls sounded as good as this 78rpm! As a rule on piano rolls, I've found that the duet performances are better for "sing-a-long" playing than for straight listening because they rely so heavily upon marimba tremolo effects in the accompaniment. The solo performances by Straight and Bargy on Imperial are always very good; sometimes exceptionally good.
The story of "Knice And Knifty" and "Ruffenreddy" really opens the question as to who was the first to compose "novelty piano solos" as we differentiate them from ragtime prior to 1917. Although Zez Confrey is usually credited as the first to compose in this style (and deservedly so, considering his wonderful compositions), the piano roll performances of Charley Straight really make a good case for him to have been the originator. All these guys, Bargy, Straight and Confrey too were based in Chicago and all of them recorded for Imperial (including Zez with his "Over The Top"). So there was a cross-mixing of musical ideas. But Straight started making piano rolls much earlier than Bargy and Confrey, first for QRS and then for Imperial. Both Bargy and Confrey had to have been influenced by his original piano roll rags.
Confrey's first commercially issued original ragtime performance was "My Pet"...unfortunately I don't have access to the appropriate research information right now, but I believe this roll came out in 1919 (I could be wrong on this and need to confirm). The tune wasn't published by Mills until several years later. Straight's QRS rag rolls date all the way back to 1914 and the Imperials (like Ruffenreddy & Knice And Knifty) date from about 1917. This makes a good case for Charley!
There is no mention of Bargy on the roll labels; in fact those rolls were probably played before Bargy worked for Imperial. When the two tunes were finally published, they had Bargy's name on the cover and a small notation on the first page of music stating to the effect "....in collaboration with Charley Straight." So maybe Charley Straight was the true originator of novelty ragtime? 
All the best,
Frank
