Good information on the flashlights you presented, made me aware of a couple I had not studied.
I would like to make a suggestion for your comparison though. When you say, for example, "The longest throwing flashlight that only uses a single AA battery is the Thrunite Neutron A2 V2. This a fantastic flashlight that is very efficient, it beats most of the other single AA flashlights in our test by over 20 meters", it is not that meaningful if you don't state which other single AA flashlights were actually in your test. You are only showing the winners, without noting what others you chose to be "in the contest".
Also, near the top of your first page, I would disagree with your assertion that the most common way to make a long thrower flashlight is to use a parabolic reflector with the LED mounted at the focus as shown in your illustration. This is actually a fairly-uncommon technique, sometimes referred to as a recoil or reflex thrower. The problem is that it is very difficult to establish a good thermal path from the LED to a heatsink while avoiding blocking the light. For filament (incandescent) lights, however, your diagram would represent the common arrangement.
Most lights will have the LED mounted on a heatsink/base at the bottom of the reflector, which improves thermal performance.
I'd say the most-common arrangements are (1) reflectorized, with base-mounted LED and (2) aspheric lens, with base-mounted LED.
TIR optics seem to be a distant third option, but it seems that it could be quite impressive if someone decided to build a large TIR specifically for throw. The downside might be weight.
