I looked at that chip but the part that bothered me is that it uses a master reset for all output bits. Individual bits can be set but not reset.
Another idea would be to use two 4-16 decoders( CD4514 ) and four quad latches. One decoder sets the 16 latched outputs and the other clears the outputs. It would take only six digital outputs to control the 16 latches. Four address lines would be common to both decoders, the fifth line would strobe both chips, and the sixth line would enable one chip to set, or the other through an inverter to clear.