Wavien collar alternative brain storming...

What if instead of making the perfect donut parabola and trying to focus it perfectly to reflect back to the LED, you cover the inside of the head with reflective vest material? That stuff is made to reflect directly back to the light source.

Would it change the color emitted?
Would a particular color of reflective material work better to produce more output?
Would this even work?
Has anyone ever tried this?
Would it all just melt with the heat?

I'm just taking a wild guess here, but the benefits might be very, very minimal. There would be very little light recycling and mostly just extra spill.