Isn’t this what you tested in the thread you linked above?
I have never had a domed LED in my S2, but with the XPL HI the narrow TIR has about the same beam size as the OP S2 reflector, but more beam intensity. The spill directly from the LED is more narrow with the TIR.
There are some more beam shots here:
Yes, I mean the 10 degree one, but the actual beam angle depends on the LED that is used. The most narrow TIR uses all of its available frontal area, so if you look into the front of it the yellow color of the phosphor will fill the front of the optic. The wider TIRs are intentionally shaped to be essentially defocused. If you look into the front of those the yellow color never completely fills the optic. It sort of mimics a smaller reflector and it causes a broader beam.
I prefer the narrow TIR. It takes some of the spill and puts it into the beam, resulting in a wider beam with similar intensity, when compared to a smooth reflector of the same size. It is a trade off though; the spill is much more narrow. But for most applications the wider beam is worth it for me.
You have to take the white plastic casing off of the TIR, and you need a suitable spacer/centering ring. I find that the convoy L2 centering ring (with the thickness sanded down some) works well for the TIRs I’ve used. Other than that it drops right in.