Uno interfacing to system with scanned keypad

Two mux'es back-to-back ? That's it !

Two 74HC4051 with common out/in connected.

Both have ABC to select the channel. So that would require 6 Arduino pins.

SiriusHardware didn't like extra hardware, but this is such a good solution. I think nothing can beat this.

Perhaps an Arduino Uno with a prototype shield and two 74HC4051.
Or a small Arduino Micro or Nano on top of a prototype pcb board.