If I'm remembering correctly, paraphenylenediamene (ppd) is the main component in hair dye, and most color developing agents are based on ppd. Ppd itself was used as a very fine grain developer, but it is extremely slow and usually causes a loss of film speed; it will form dyes in color film, but it's far slower than a real color developer.
Betadine appears to contain iodine. C-41 developer contains some form of iodine, which I think is used to keep the dye layers developing at the proper rate so the colors are accurate. Though that may not be the purpose of betadine in this formula since the colors are obviously not accurate at all.
I don't think caffeine would form dyes in color film, but it's certainly worth a try. Many things will form a color image, for example, p-aminophenol (the developing agent in agfa rodinal) and phenidone (one of the developing agents in xtol), but any developer other than the "real" one will give you incorrect colors and probably a very faint image.