Have you considered spending some time working on playing snare parts, without any other drums? If you do that, you could play them over a "boom chick" on the kick and hats if you need to keep time for the band. I don't know much about Jazz, but I think that sound was associated with New Orleans Jazz. If you pulled that together and then added accents on toms and cymbals, that might be something. You might spend a while developing the sound before a song came along where it really worked, but it could be nice to have in the toolbox.I was wondering if anyone has a good idea on how to stop keeping time with the right hand on cymbals and hi-hats.