One thing seems odd: it takes an 800W LED to double the light output of a 250W halogen bulb. Normally LED is far more efficient than halogen so I wonder why the opposite is true for this project.

I agree, this seems really odd. The solution should not be a modern projector with 1kW electrical power converted into heat.

The Cob array of leds is the problematic choice, while on paper you get a lot of light, you don't get a point source.

If you look at the large theater projectors, I remember laser sources (but no speckle, is this pumped phosphor?) or expensive xenon bulbs. At least 10years ago...

I remember a solution (car headlights?) of decoupling the phosphor (for converting uv to while light) from the UV Led. So you have multiple diodes pumping a small piece of phosphor for a nice bright point source. Not sure how this can be replicated open source.

Another approach (studio led lights) wasomething with glass mixing rods? You insert the light of multiple leds into a glass rod, and a uniform beam emerges. But I guess this was more to improve CRI, rather than to increase brightness/point source.

An 800w LED is not as perfect a point source. They are loosing lots of light that isn't focusable. See how in the comparison picture that there is insane light bleed out the side from the LED projector. The older projector benefits from a hundred years of optimization of how to focus a lightbulb into an image. The LED rig is starting from scratch with a source that isn't meant for focus onto an image.

The discrepancy likely stems from projector-specific optical constraints - while LEDs are more efficient at converting electricity to light, they emit omnidirectionally requiring complex collimation systems that lose significant light, whereas halogen bulbs with parabolic reflectors can direct most of their output through the projection path.

The LED lamp system they built looks like it was designed by an overclocker.