Think of it as fun. 
You've said you are low on input pins, so something must give.
Either you do the 12 pole switch differently than one input per pole, or you move the hole thing to an Arduino with so many i/o pins you'd never run out no matter what you needed to do.
Looks like three possibilities
- use more i/o pins
- use one pin and a bunch of resistors
- use four pins and a bunch of diodes
If I had four pins, I'd use the diode encoder. I've just never liked the analog one pin hack, but I must say having been participate on the other thread @camsysca linked, it looks like sometimes it could work well:
resistor analog switch decoder
Your party, your rules!
a7