[Al Skierkiewicz]

Guys,
Generally caps are not going to fill in the current needed for the length of time that the battery browns out. You can very easily use a LM317 three terminal regulator as a custom circuit set for 5 or 6 volts with just two resistors. If you connect the reference terminal to a digital output, you can turn the supply on or off. Then it is a simple matter of wiring your LED string for the voltage you have chosen. Please remember to isolate and insulate your custom circuit.