I am not sure what your goal is for "regulated" or not for a 3 x AAA. Just MHO, but most converters need at least 1 V of headroom above the LED Vf in order to be useful, or you are just as well to use a resistored light. With 3 x AAA, you will be lucky to have > 0.5 V above the typical Vf of a Lux III, especially if it is reverse battery protected.
I would spend the extra money on good batteries with a flast discharge curve.