As you can see, the red and green LEDs are tied together at the anode. According to the datasheet, the voltage drop across the green LED is 3V@20mA and across the red LED, it is 2V@20mA.
To drive the display at 20mA through each LED, I can put a resistor at the anode of the LEDs (pins 12, 11, 10, 4, 3, 9, 6, 5) and an additional resistor at the cathode of the red LEDs (pins 14, 13, and 8) to compensate for the lower resistance of the red LEDs compared to the green LEDs. However, for each red LED that I turn on the 20mA of current will be split between them. This will make the red get dimmer for each red LED I turn on. In this case, an "8" on the display would be way too dim to read in red.
The other option I have considered is putting a network of BJTs and parallel resistors at the cathode of the red LEDs. Each time a new red LED goes on the BJT connects a new resistor in parallel, lowering the resistance at the cathode of the red LEDs and allowing more current through the LEDs of the digit. This approach seems to work; however, it adds a huge amount of new components (48 more resistors and 24 more BJTs) and complexity. I would like to keep the number of components as small and simple as possible. I am looking for a simpler and more compact solution.