Is it possible that the wires pick up so much by induction, that a shot knocks the MCU (ARM SAMD21G18) unconscious?
Yes.
I hesitate to use capacitors to not affect the sampling speed...
These are contact closures!
You are not going to affect anything in regard to your sample rate, they are way too slow.
I would use catching diodes to both rails along with a 1K pull up on all inputs.
http://www.thebox.myzen.co.uk/Tutorial/Protection.html