i used the rhythm circuit for jazz band in high school. it sounded great, i didn't mod anything (it had a mustang bridge at that time i guess). just roll off the tone control slightly (but the rhythm circuits pretty muddy anyway). then it's about how you set the amp (believe it or not, it's easier in the long-run to just use solid-state for jazz, especially if you're in a combo or big ensemble or something).
i used the jag-stang for jazz band at a couple shows, i have pics somewhere!