mouldy.org

At a guess, I'd say that your Luxeon III"s are being run at about 1A. Cree XR-E's should handle that. Most LEDs will tolerate overcurrent anyway if they're well heatsinked.

You should be able to just plug the XR-E's in in place. The main challenge then is the physical installation. If you've got Luxeon III Stars, you'll need to get a Cree 'Star PCB' and solder the LED onto that. If you've got Luxeon III Emitters, you'll need to figure out how to remove the old LED without damaging the board - which I expect will be challenging.

Constant current power supplies are just what they say - constant current. The resistance in the circuit is irrelevant because the power supply will adjust its output to always have the same current. This is assuming that it's using a constant current power supply at all, but odds are good that it is. Resistors are too wasteful to use in this sort of application.

I think it'd be worth a shot, but there is a significant amount of risk there. New lights with XR-E's are becoming quite affordable, so a brand new set might be a better option.