You will always have a somewhat eratic idle RPM when your are playing music, because the regulator will be telling the ECM to increase and decrease idle RPM as every bass hit passes.
The low voltage at idle problem could be improved by decreasing the alternator pulley diameter. The idle RPM will still change under a load, but you will start off with better voltage. We custom machine 46mm pulleys in house, they are the smallest you can use and still get a nut on the rotor.