Beebauman, I have an older Casio that does exactly what you want. With Casio Chord on, it has a row of instruments dedicated to the chord. So left hand chord instrument is independent of right hand instrument. There are only 12 instruments, but this was a cheap keyboard. I hope the more expensive models didn't cut out this feature. I have a Yamaha with the same issue. The chord mode only plays 1 instrument - an electric organ sound.
David