Hi, Tony,
Yes, you can modify the sandwich in the FF with a LuxIII without changing the electronics.
Remove the module from the head of the light by removing the snap-ring with the proper pliers, then shaking gently to remove the module. Unsolder the leads of the existing LD luxeon, (take note of positive/negative connection), and remove it from the sandwich. Clean off the old Arctic Silver paste, and put a fresh coat on very thinly. Replace the stock Luxeon with a LuxIII and resolder leads, making sure the polarity is right. When soldering into place, the Luxeon must be centered on the sandwich, so it sits centered in the optics when you put it back in the FF. If it turns out that Wayne uses heat-sink epoxy to glue the Luxeon down instead of using thermal paste, you will destroy the stock Luxeon and possibly the sandwich by removing it. I've never done a transplant, but this is the procedure I would follow if I was to do so.
Contact Wayne at the Sandwich Shoppe or Wayne at Electrolumens for LuxIIIs. They are a bit hard to come by at present, so you may have to wait awhile. You would want the bare emitter.