The Cree is a tight fit, since you need to flip the heatsink over or else use a platform of the right height. Either way, the focused Cree is very close to the reflector, leaving not much room to attach the wires. Fortunately, the back of the reflector is anodized and will not short.
The Luxeon III is a drop-in mount for the KL6, so the SSC will fit if you use a shim to raise the emitter to the same focal height as a Luxeon III. Fortunately again, the heatsink is anodized, so the infamous positive slug won't have a shorting risk.