I agree that with a given diameter, you can vary the 'focal length' of the parabola, giving the light a different beam pattern (but does not affect throw much), a longer focal length makes a shallower reflector, a shorter one a deeper one. I do not agree that there is 'half a dozen' parameters, just four actually: diameter, focal length, surface texture, and size of the hole, the last one does not even influence the optical properties. 'How much of the back is omitted' is not a variable, it is fixed, directly related to the focal length of the parabola, if with a given focal length you are going to vary that, you are just bringing your led out of focus.
You can always of course leave the parabolic shape of a reflector, that will destroy the brightness of the hotspot very effectively, but it can be done to obtain a wanted beam shape.
I’m rather curious if people do the focal ring thing instead of focal point. It would make sense, since the LED has non-zero dimensions, so it could focus more of the light more accurately. However, it would also make the reflector specific to a single size of emitter.
Basically, cut the parabola in half down its axis. Shift the two halves apart by, perhaps, half the width of the emitter. Extrude that shape around the axis to make it three-dimensional. Now you have a reflector optimized for a light source of a specific size.
As I understand it, the problem lies in the size of the dies. The tiny XP-E die face makes for a more pinpoint source of light which results in an accurate gathering of it’s output by the parabola for emissions in a tighter profile resulting in increased throw by default of the smaller hot spot. An XM-L die is significantly larger, the point source is spread out such that the parabola does not see a single source of light but instead a conflicting broad flat panel with emissions diverging from sources too far away from center to be accurately collimated. Hence, a much larger hot spot with less concentration of output. To answer the broader source, a much larger parabola is required to minimize the effect of the point source being so large.
Bucket is working on creating his own reflector and has experimented with vast research on the subject, in an effort to effectively focus the broad emissions from the large MT-G2 emitter with hopes of enhanced throw characteristics from an heretofore floody source. With a new process in place the expected results should surface soon, I believe he’s working on this even today. His thread” DIY Reflector”:DIY Reflector is an interesting read at the very least, and pictures showing his progress are invaluable in accessing ideas pertaining to this subject.
As in so many other discussions, there are opinions a-plenty. 
if you want to play a bit you can add this : http://www.cnqualitygoods.com/goods.php?id=1396 on the top of your stock lense ,it fit almost perfect.
i build mine with dedomed xpg2 @ 4+amps (direct drive with 20R) and its a monster
i was lucky that i had already this pill http://www.fasttech.com/products/1616/10002799/1208600 (added some copper inside it as well)
i really liked that host , i would like to test it with XP-E2 on copper as well.
You put an aspheric optic into a BLF C10? Or was it some other host?
How was the focus?
Did you remove the reflector? How did you hold the optic in place?
Any idea what the resulting throw was?
yes on the c10 ,i but it on the top of the stock lense and kept the stock reflector.that plastic lense is almost perfect fit ,after i installed it it wont fall.
the beam looks small but stronger ,unfortunetly i dont have any equipment to make measures.
some ceiling photos ,i dont know if they help
Oh, okay. So, the beam looks something like this?
The above was created simply by holding an aspheric in front of a traditional reflector-based light:
yes it does but in 3-4 meter range,i’ve added some photos.have in mind my led is not perfectly center.
Heh, the contrast in that beam pattern makes it look like you have a circular hole in your ceiling around the hotspot. It’s kind of a neat effect. 
anyone moded this with mt-g2 ? …
If I recall correctly, a few people have put a MT-G2 in a C8, and some have done it in a Convoy M1… but that would require 2x18350, a zener mod on the driver, cutting the reflector to make room, and maybe some other changes. And it would be almost entirely a flooder, not a thrower. The BLF C10 was designed to be a thrower.
So, it can be done… but the purpose is entirely different. And I think the MT-G2 alone (on copper) would cost about as much as the C10 host plus all the parts to mod it.
you can skip the 2x18350 with this : https://www.fasttech.com/products/1575200 (its not perfect fit with c10 but its not bad)
sure mtg2 will cost 2x the price of the c10 host + you will need a driver