I found this site the other day:
http://dmcleish.com/CPF/Spherical-Reflector/index.html
It set me thinking about that setup. With aspherics you get no spill, the light coming out of the sides of the LED is wasted and contributes nothing to the beam. With a reflector, light going forward out of the LED misses the mirror and goes out as spill, its not wasted but contributes little to the spot. With that reversed diode setup all of the light coming out of the diode reaches the mirror (although some will be blocked by the LED / wiring /support).
If you design the mirror and make it with good precision I think one of these could outperform an aspheric. Who is going to buy/mod/make one to prove it?
Heatsinking was the problem I could see, I thought that if you made the lens out of monocrystaline diamond it would probably solve the problem, failing that an aluminium bar from one side to the other carrying the LED in the centre could remove some heat.