I have found a way to add more digits to this installation. The key is to put a common anode seven segment display in parallel with each common cathode existing display. The capacity is instantly doubled to 18 or 20 digits maximum.
-8 pins on the Arduino connect to the segment pins on the seven segment display.
-9 select lines connect each of the common pins back to the Arduino.
-On the 8 pins used for the segments, connect 9 common anode displays and 9 common cathode displays.
-each of the select lines goes to the common anode of one display and the common cathode of another display.
To illuminate one digit, put the pattern on the segment lines, using 1 for the segments that will illuminate, then put 0 on the selection line for a pair of digits. Then put another pattern using 0 for the segments that will illuminate and put 1 on the selection line for that pair of digits. Lastly, put the selection line in input (high impedance) and move to the next pair of digits.
Using this technique a tile can go from 9 digits to 18. To keep the square form factor, lets do 4x4, using 8 common anode and 8 common cathode displays.
Parts have been ordered to test this technique...