Thanks for all the feedback. To respond to some of the points:
1) I intentionally didn't change anything as per manual and went out in that hot temp with full stock setup because I wanted to discover what is the limit of the stock system if I were to push it on the street in the setup how I drive it every day.
Now you know what's not nearly good enough. A 50° cooler ambient isn't going to make all that much difference when you're seeing 800+ at the rotors/pads/calipers.
It's not clear whether your fade was pads (hard pedal) or fluid (soft pedal). But I wouldn't take a car of this weight out on track with anything less than Carbotech XP10 or G-Loc R10 pads, Motul RBF600 fluid, and some kind - any kind - of supplemental cooling. You have to be able to trust that your brakes will be there for you. Every time.
2) Ultimately I don't want to use anything "track specific". I'm one of those guys who wants to come to track, drive, and leave, without changing anything. I dislike the idea of having some slicks and different cooling when you're out on the track. I want my car to handle the same regardless of track or street - I don't want to learn 2 different driving modes. Just a personal preference I guess. Especially I hate the idea of these brake ducts that "expose the brakes to the elements". There's a ton of sand and debris flying around the track; it's the last place I want to expose my brakes.
3) However, for my next track day, I will certainly put in higher temp fluid and will swap out the pads for something higher temp. We'll see how far that gets me without brake ducts.
If you don't want to swap pads (which I understand), you'll just have to put up with the downsides on the street of pads that are legitimately track-capable. In my experience, Carbotech XP10 pads (or G-Loc R10's) ought to be enough pad for your track time while still having sufficient cold bite for normal street duty. You'll just have to be prepared to deal with some dust and at least occasional noise.
You don't need slicks at this stage, but if you're going to stick with this you really should invest in a dedicated set of wheels and tires for the track time. Any top-shelf max performance summer tire will be enough. Hint: mount the track setup on your car when you bleed your brakes in preparation for each track day/weekend, and bring two of your street wheels/tires along in case you get a flat on a track tire or run it down into the cord.
4) When I say "experienced complete break failure" what I meant is that when I rolled out to parking lot in 1st gear which would go less than 5 mph, I couldn't stop at that 5 mph using brakes - they did nothing; I ended up resorting to the parking break to stop the car.
A car in that condition should not be out on the track.
5) This picture probably does have me breaking into a turn
If you were to get completely off the brakes at or a bit before that point, the car should turn in very, very nicely. I wonder if you might have been a little 'early' there.
6) is 2:08 a good time? I think many cars run less than 2 minutes there. I could've easily done less than 2 minutes with working brakes. I set that 2:08 time in the first 3 laps of the day where I overheated the brakes. It was the first time I ever drove this car on the track, and while I braked aggressively, I by no means pushed the car to the limit. I was just exploring. Plus traction control and a passenger. After that, the rest of the day I set 2:10 time on 90% of laps using almost engine braking exclusively (and a little excessive sideways action, which was fun for my passenger

. I actually enjoyed purposefully not using the brakes as it felt like go karting where I have to focus on carrying maximum speed through the turns. There was a last gen Corvette Z06 in the same group who I kept passing and it felt like I was cruising, while he was trying so hard, almost flying off the track on every corner. I don't have much experience on track, maybe have been total of 10 times on 3-4 different tracks. I do have a lot of experience on the street though (in a safe manner of course).
8 seconds in two minutes is an eternity, particularly given that you're only seeing 2 or 3 seconds difference between the laps with full braking and those where you were intentionally going easy because of reduced braking capability. 2:05 would be a much more realistic expectation at least for now, and it might be harder to get there than you currently think.
7) Interesting conclusion to this story - yesterday my car rolled backwards in parking lot and hit another car. I had it parked on incline with only the parking brake set (didn't put it in gear, from now on I will). It engaged and held the car for some time, but then simply released. The damage is minor - just some scratches on rear bumper, but could've been much worse. I wonder if this is related to what I described in #4.
Regards