Hi Matt,
A few issues I noticed:
(1) This is just a matter of terminology, but PWM stands for Pulse Width Modulation. The regulators you have listed are linear regulators ... they don't use pulse width modulation.
(2) Steady state DC current flow through a capacitor is zero. So the circuit will not work with the .33μF & .1μF capacitors connected as shown. Instead, they should be connected between ground and the regulator's input (& output) terminals respectively.
(3) Linear voltage regulators need a bit of "overhead" voltage to work properly. The NTE1970 you have listed requires a minimum input voltage of 14.8V ... see specs at:
http://www.nteinc.com/Web_pgs/Positive.php?a=12 Even their low dropout NTE1954 12V regulator requires a minimum input voltage of 13.6V (
http://www.nteinc.com/Web_pgs/pos_lowdo.php?a=12) It's very common for the voltage in a vehicle to drop below that level.
Having the input voltage go below the regulator's minimum requirement won't cause any harm but it will cause the output voltage to sag and therefore your LEDs will be dimmer than normal. So you might want to consider using lower voltage regulators and re-calculating your current limiting resistors to work with the lower voltage. That might also require reducing the number of LEDs in each series string.
Another alternative would be to directly regulate the current through each string of LEDs to the required 20mA. Take a look at the "1A Current Regulator" example on page 16 of the LM317 datasheet (
http://www.alldatasheet.com/datashee...NSC/LM317.html) for an idea of how to wire it as a current regulator. You'll obviously have to change the resistor from the 1.2Ω for their 1A example. You can calculate the value using Iout = Vref / R where Iout is the current, Vref is the LM317's 1.25V reference, and R is the resistance. So for Iout = 20mA you'd want 20mA = 1.25V / R. Or R = 1.25V / 20mA = 62.5Ω. The only catch with this method is that you'll need a regulator for each series string of LED's.