Thanks Rick. Cute little design. H.O. (to borrow an automotive term) LED and wide flood angle (35deg) - looks like a nice LED - perhaps one of the newest generation of 5mm LEDs (like in the Photon Maxx) ???
Improving just a bit, but still keeping it quite simple so no regulator circuitry is required, I think I'd like to go for a double-throw switch. Why?
Put the 27ohm resistor on one side of the switch for when batts are fresh and near rated voltage, then put a lower resistance resistor on the other side of the switch for when the batts are closer to 1.0-1.1 volts (1.2v???) for each cell. This will give a "new life" to the LED, making it brighter again, but for a shorter overall burn time - not that much usable light is available near the end of useful batt life anyways, so, not really much of a loss, IMHO.
Possibly could get by with no resistor - need to be careful NOT to switch to this side before batt voltage drops significantly - i.e., closer to the forward bias voltage. Like zener's white LEDs have a very narrow band where they respond somewhat linearly to voltage - too little = no output; too much = exceed max sustained current capability and will burn up. [sort of an "avalanche" region] Need to operate in the narrow band between the too little and too much voltages (around rated forward bias voltage, typically ~3.4 to 3.5 volts for white LEDs, IIRC - best check me on this) in order to operate without a current limiting resistor.
I've done something similar with a double-throw switch in a homebrew 9x5mm LED array headlamp I made a few years ago, but not for switching resistor's, but rather for switching in a backup set of 3xAAA batts (3xAA were the primary source). when the primaries were run down.