Am I drawing too much power from the board?

I'd leave the final resistor values to the user, according to the really used LED and supply voltage. 10R look a bit low to me, the resulting current will vary heavily with the supply voltage.

I'd start with 100R and many LEDs in series, then reduce the number of LEDs until they light up. Then adjust the resistor value for the intended brightness, but not below 22R.

Some people suggest 1k base resistors always, to safely saturate the (small signal) transistors. Power transistors, with less amplification, may deserve lower values, or another driver stage.