Oh good, I was hoping to find someone that had experience using the LM317.

My last LED project was illumination of a custom boost gauge in the Supra. I was using 3 white LEDs in series with a resistor, much like the diagram in my first post. Problem was, the guage was barely illuminated with the engine off and the brightness would get noticeably brighter with an increase in engine RPMs. This is what I was hoping to avoid by using the LM317. If you take the voltage, subtract the voltage drop from the LEDs, then divide by the resistor rating in ohms, you can calculate how many milliamps you are running the LEDs. At 11.9 volts (engine off), you get 16.2 mA, well below the recommended 20 mA for this LED. At 14.6 volts (engine on), you're at 26 mA and overdriving the LEDs by almost 28%. This is why their brightness varied so much.

Did you simply use the R=1.25/I formula and throw whatever resistor this equation calculates for each array? (I can't see the LM317 in your pics.)

When you say the brightness varied dramatically, do you mean the LEDs were brighter when you started using the LM317?