I just had a flash of brilliance, but it's making me feel really stupid. I probably should've explained what I was doing first. I want to run this LED off a Li-ion 22.2V (6 cell) battery pack. The reason I'm wanting to do it this way is so I can keep the LED at a constant brightness until the battery pack is completely drained.
So for my flash of brilliance: Being that these are Li-ion cells, they can't be discharged down to less than 2.3V, this being the case, my battery pack as a whole can only dishcarge to 13.8V.
Obviously this significantly decreases my specifications. So what is THE most efficient IC that I can use? The more efficient this is, the less of a heatsink I'll have to use too.