I partially assembled the board - only 7 CD4051 and one 74HC138 were populated. Then I removed transparent keyboard circuit from calculator remains and soldered 15 wires to his "brain":

Added 2xAAA power source (3V) and magic - it worked :)

I even changed code a little on JP2 inputs and it printed something ;)

So it looks like it is right direction for further experiments...

P.S. Just uploaded Eagle files (with Gerbers) to the project