There's probably some clever IC out there that will do what you're looking for. The attached circuit is my completely untested, unproven idea. If you use it and it breaks then you get to keep all the pieces.
It is basically a Joule Thief, self resonating circuit hooked to a shunt regulator. The shunt regulator will be set to an appropriate voltage so that it pulls the N-channel MOSFET's gate up enough to completely turn it on and keep it out of its linear region. (5V to 7V, should work.)
It probably isn't particularly efficient but the nice thing about the Joule Thief circuit is that it is known to start-up and work under low-voltage situations. It will start-up and run even when a single cell gets down to 0.7V to 0.8V.
The cap across the shunt regulator will have to be big enough so that it doesn't cause the shunt regulator to oscillate. (They don't like certain sized capacitive loads.) A zener can be used instead of a shunt regulator but wouldn't likely be as efficient.
You would have to wind your own (tiny) transformer if you use this method. So it would be practical only for small quantities. Use a small toroid ferrite core with as high as flux density you can find and put as many turns of 30 AWG magnet wire as you can get on it for the primary and secondary.
Some of the component values may need some tweaking and the particular parts used aren't critical. The BC337-40 can be any NPN BJT with high gain. The 1N5818 can be any Schottky diode.
Edit: I forgot to draw the arrow on the MOSFET but, as noted above, it is an N-channel. Also, the resistor on the base of the BJT can probably be made bigger to improve efficiency. You just want to be sure you keep the BJT saturated when it is switched on.