I would like to preface this by saying that I'm just a hobbyist, and most of what I say is just stuff I've thought about. I'm really just hoping to flex your brain a bit while we wait for someone more knowledgeable than you to arrive.
You are using an LED ray source? I would guess that you wouldn't really look at how the rays exit the TIR, but rather how they would project at a couple of distances might be easier? Ideally, a collimator would have all exiting rays parallel. Of course, this isn't possible with something as big as an LED as a source, and nobody said that all TIRs must only be narrow angle collimators...
The way Carclo seems to do it is by using the "reflector" surface to create a hotspot, and then capturing the spill using an appropriately sized aspheric element in the center, whose output is overlayed on the aforementioned reflected hotspot. I think since the diameter of the aspheric element is much smaller than the "reflector" surface of the TIR, the output is a larger spot, so it adds to the hotspot, but also produces a corona around the hotspot, which some people note as a square image of the LED.
Internal rays I would think just to make sure that whatever doesn't hit the reflecting surface hits a refractive surface. Khatod uses a convex lens on the inside, while carclo appears to use a convex or aspheric on the top side. I think a lot of the final output shaping is done by the front surface, either by microlensing or just texturing.
When looking at the rays exiting the lens, I think the farther they are from the center, the more likely to be accurately collimated. In different words, a higher percentage of rays from the LED will be within a smaller range of angles if they reflect off of the back surface farther from the source, while the rays that hit the reflective surface closer to the source will be able to reflect at a larger range of angles (because the image of the source from that point is bigger, so rays can come from a larger range of angles). SO, with that said, I think the best visual inspection would be to look at the rays exiting the lens farther from the center to make sure they are going where you told them to.
This is an interesting project, and I really really hope someone who actually knows what they are blabbering about will come in and set me straight, but maybe for the time being, this can get your brain to find the real solution ;-) I seem to remember member RA hand-crafted some glass TIRs a while back. I think he focused mainly on the reflective curve than on the front or inside features.