I am obsessed with doing it. I also play, by way of example, some Chopin studies and rags by Joplin and Scott. However, I cannot produce an improvisation which comes anywhere near a decent imitation of pieces by these people
Oh, I wasn't intentionally trying to be dismissive. As a matter of fact, I have the same issue with doing "in the style of" Joplin and so forth.
I have no qualms about taking any of Joplin's pieces and just sort of "ragging" it out, messing with the melody, introducing little flourishes, but I suspect a lot of the difference is that Joplin is so specific about voice leading and which chord inversion to use. "Solace" is a great example that comes to mind -- thats probably one that should be played pretty close to how it's written, even though once you understand the three chords or so, you could (not should, mind you) just fake it.
To contrast with another one I've been just fooling around with (I know it's basic, but I'm not a dixieland player at heart), just "Tiger Rag"-- that's easy (for me) to mess around with, and steal some tricks from various Jelly Roll performances.
The difference is, it seems, that little pieces like "Tiger Rag," and others that, even though they were published by various companies, and sometimes have canonical performances, or at least performance practices, are sort of "up in the air," in a way that things like, I don't know, the Joplin pieces or, .... I remember a Hamelin encore of .... what's it called....the.... "Kitten on the Keys" (fun tune, not too hard, a pregnant dog to remember) are not.