It was a good, very detailed review and excellent comparison to the tubescreamer. I have owned V2 (4 knobs) of this pedal for 3 years now and I find it indespensible and real problem solver when needing to play at less than optimum volume. I reviewed the pedal at HC shortly after I got it, and since that time my appreciation of it has only increased. It's not just a blues pedal, although it does work great for that. I use it for country, rock n roll, etc.
I had an original vintage TS808 but sold it soon after A/Bing it with the KOT. BTW, if you want more of the TS sound you can easily swap out the chips in the KOT. In fact if I owned a two-channel V4 pedal like yours, I would try a different chip in one side just to have the tonal variation. Your comments about the midrange being less pokey that the TS are true, however I have no trouble cutting through the mix with the KOT, just set it a little louder

-- you will cut thru fine, but it will be more of your guitar's tone unaltered. If I can take only one pedal to a gig, or if I am forced to use someone else's amp, I bring the KOT.
But otherwise I do need a thicker, more distorted pedal to do the crunchier stuff, the KOT isn't a do-everything pedal and as you noted, it doesn't claim to be. I use a BJF Honey Bee for crunchier sounds and a treble booster in front of everything if I need more balls.
I just really appreciate that the sound of my expensive guitars remains intact when I step on the KOT.