Why not take 2 (or more!) identical keyboards, and connect one membrane to all the encoder circuits? It may require some additional passive components to limit the voltage/current, but I can't see any good reason why it wouldn't work.

Very cheap multicast keyboard solution? Can't find that this has been done anywhere...

Here's an image I found, to give you a better idea of what I'm talking about. Basically disconnect input set X and Y on all the keyboards, then connect up all the encoders to just 1 key membrane.