How to connect a large number of multi-throw switches efficiently?
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Since accidental contact closure is not an issue the switch contacts can simply be wired in parallel for redundancy.

Using this arrangement any multiplexed configuration including charlieplexing can be used. I don't think you can use less than one diode per switch except for switch 17 (4 x 4 + 1) as it may be on it's own dedicated pin. That makes 16 diodes the minimum.