Not really….
Firelight is right. (I like the sound of it). Throw = surface luminosity * area. Even if some light escapes to TIR sides - the light from the centre of the emitter doesn’t. And the centre is what produces the hottest point of the beam. Higher surface luminosity always wins.
With TIR it’s slightly different because they are produced to focus an emitter that’s placed at certain height. If one emitter has different height than another - the one with lower surface luminosity might actually win as long as it’s closer to the designed height.
However modifying optic’s legs should fix that.

So White Flat would be the best emitter.
However with Carclo - the host will overheat FAST. A Synios might be a better option………but focusing that is going to be a challenge.