Method for selecting unique resistor values in all combinations
With a 8 bit ADC , you can easily gang 6 switches in a binary R ratios.

ADC's normally use SPDT or dual voltages or currents.  But you have SPST contacts.

Rather than E10 values which have only 10% tolerance, you can choose the nearest 0.5% values of; 1k,2k,4k,8k,16k,32k

Proof of concept