Pat, why will it hum? All those are line levels already right and isolated from the chassis?
If it was me, I'll tied all the input ground together then the two outputs on their own then connected to the same ground bus connected to the chassis or the board signal ground. Or, you employ localize grounding assuming that it's okay if you do not mind having several wires crossing the chassis.
You can mix or match grounding schemes. Aesthetics wise, it is simplier to follow what grounding scheme the circuit already has (PCB).