Thanks for your replies.
" Also, ideally I'd like to switch the LED as fast as possible (clean square wave in the 10's of kHz range), which the transistor solution lets me do."
Not really sure what intended here - unless it was the switching speed of a boost converter:
"The LTC®3490 provides a constant current drive for 1WLED applications. It is a high efficiency boost converter
that operates from 1 or 2 NiMH or alkaline cells and generates 350mA of constant current with up to 4V of
compliance. It contains a 100mΩ NFET switch and a 130mΩ PFET synchronous rectifier. The fixed switching
frequency is internally set to 1.3MHz."
the LTC3490 looks quite nice, its a bit expensive in small amounts and of course a pre-assembled "typical application" module would make things easier, but it's the best option so far. I think I'd have to use 2 cells though. With one, the LTC3490 efficiency drops to 50% and drawing 1.5 amps from an alkaline AA will drastically reduce its capacity. That's not a huge problem though, and as far as your later post, the LEDs I have in mind require 350mA in the 3-3.4V range, so it appears this is the right chip for what I'm doing.
I'm actually thinking of a few projects that involve switching the LED, the more complex involves carrying data. Imagine people carrying flashlights and I can identify them by a signal carried on the beam. Like an IR remote but visible with a high-power LED. The simpler project is a stroboscope, an external trigger turns the LED on for 50 to 100 uS.
I'm not familiar enough with these power supplies, can I just use a transistor to switch the output and when I want to turn the LED on the power is there and stable fast enough?
Unless I'm mistaken, I think he asked for a PWM solution?... there are plenty of other ways including a switching regulator for a couple of bucks off of ebay (this is the most efficient way though for the price) but feel free to play with the 555 if you want a cheap solution to make your circuit more efficient.
I still don't understand how PWM helps me get a constant current to the LED.
You mean use the power supply you linked and a series resistor so the brightness is more stable than just directly from batteries with a resistor?