If I understand the design you have correctly, it is essentially a PWM (pulse width modulated) output which means that it doesn't actually "regulate" the voltage level, it pulses full power very quickly and the motor "averages out" the voltage to go a specified speed. For example, if you were to set 30% throttle, the SCR will pulse full voltage for 30% of the time and zero volts for 70% of the time. The motor response is slow enough that it will average the voltage out and go slow. Increase the speed and the full voltage pulse gets wider, putting out more "average" voltage.
That being said, it is surprising that an LED would blow immediately assuming the LED is properly current-limited by a resistor. If not, then for sure it would blow - an LED is a lot quicker than a motor and is unable to average the voltage out. Plus it can only take a small amount of current (generally 20mA or so). If you were to install at least a 500 ohm resistor (prefer 1000 ohm), it would limit the current to the LED and prevent the blow out. The LED would run somewhat dimmer though. The only other way would be to install a 3.3 volt regulator between the LED and the power - that would stabilize the power and reduce the voltage to the LED.
Mark