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comment K out of N encryption
The redundancy approach is actually exactly what is used by the suggested approaches.They avoid revealing any actual bytes, but if the message has entropy H in an K/N scheme, each person does get HK/N bits.
comment Is there a secure cryptosystem that can be performed mentally?
You could also change the RC4 state to the 56 of a deck of cards. Skip all the tedious rc4 initialization by simply shuffling the cards. Give Alice and Bob an identical deck. For the amount of communication they should be able to do by hand, they can just continue with the same cards as long as they manage to keep in sync.
comment K out of N encryption
Sure, I believe the idea is from knut theory. Say you have one wire to which the 'gold' is fastened and two padlocks. You want that if either of the locks are opened, the 'gold' wire is completely freed. You do this by letting the golden wire go first clockwise around the first, then clockwise around the second, then anticlockwise around the first and finally anticlockwise around the second. It can be thought of as aba^-1b^-1. If you remove either, the other cancels out. It generalizes to any k out of n padlocks.