I've done quite a few KL4 mods as well and a number of them were using the stock driver. Since the stock driver is a boost circuit, the general rules of boost circuits apply to the stock converter too. The Vin cannot exceed the Vf of the luxeons. By Vin, I mean actual battery voltage after sag under load. What this means is this, and this applies to the KL4 circuit only. Not boost circuits in general.
Without any modification, the circuit will deliver about 350mA to the lux III on a single 123. If you drive it with a Pila or other li-ion cell, then it will deliver the full 660mA to the luxeon III. The board uses a .33 ohm resistor as a current sense. If you run a 1 ohm resistor in parallel with this, you'll get about 500mA to the lux on a single 123 and about 1A on a li-ion cell.
Just swapping the emitter is the easiest way to mod the KL4. It runs fine as long as you don't try to feed it with 2X123, which will smoke it.
The best way to do it is to replace the stock converter with a Wiz2. That way it'll run on 1 or 2 cells, but it's much more difficult. The way I did it was to fabricate a replacement circuit housing, but I haven't done it in so long that I don't remember what I did with that drawing with the dimensions.