Hello: An “acoustical engineer” could help, but short of that expense, a few more suggestions are to dense pack the walls with cellulose. Add resilient channel then add another layer of sheet-rock. Seal off any air leaks between closet and indoors as these are also good paths for sound to travel. Install a mount from the floor to support the heater.
But first, ask Rinnai what the hum could be and how to get rid of it. There is a small chance it’s something in the unit 😉