Understand, I have asked the same question!
All I know is if I don't turn off traction control I get the smell of my clutch and rpms climb due to my clutch slipping. Not sure myself.

Is this in a straight line situation?
I wonder if this is an indirect result of the DTC maybe becoming confused if the front wheels are spinning???

I am assuming that you are pressing and holding the DTC button to turn all of the traction controls off. So, another thought. Have you tried just pressing the DTC button quickly and not holding it down? On my MINI the word “Traction” shows up in the Tach. I find that works well on the track as it cuts down the agressivness of the traction control. It may help with your issue.

I was thinking that was the case; the DTC has nothing to do with the clutch. But it seems that in ridinDirty’s case that the DTC is doing something to, maybe, cause a wheel or wheels to drag. Truly just guess here, But I did have a problem with the DTC on my S when I put the BBK in. The eLSD part of the DTC would be overly agressive and over-brake the inside wheel in turns and the wheel would literally drag through the turn. I then found that MINI does a modification to the DTC computer program for when the JCW sport brakes (the Brembos) are installed. I made that change and things are better now. Not saying that is ridinDirty’s issue; just that modifying these MINIs may have unintended consequences. For example, does the added power, with a LSD installed cause “confusion” in the DTC system? Could there be some torque steer that is causing the DTC thinks is the car going into a spin and the DTC is applying the rear brakes to correct the spin, causing drag on the clutch? I don’t know. Interesting issue, though...

I had an ‘07 too. It didn’t have DTC, just the traction control. It seemed that it would just cut power when the wheels slipped. No braking, the way I remember it. I tested it a lot in the snow. I remember going to a ski area and wondering if it would let me get to that area when it almost slowed me to a stop. I also seem to remember the button was an on-off switch, like yours. Of course none of thiis was at the level of power and torque you are at. Not trying to ”fix it” just wondering. Interesting....

Which LSD do you have?

Very fair question...
Wilwood has several BBKs for the Gen I and II MINI Coopers, and TCE Performance Products has some of their own variations of these BBK which makes for a wide range of BBK products for the car. I have the smaller of BBKs that they have available and it is made in two rotor sizes, the 11.75” and the 12.2”. The calipers are radially mounted and only use a spacer to accommodate the larger rotor. There are a number of aftermarket 15” wheels that fit very nicely over the Wilwood BBK with the 11.75” rotors and there are a number of 16” wheels, including MINI wheels, that will fit over the BBK setup with the 12.2” rotor. The Wilwood BBK as marketed uses a 0.81” thick rotor (basically the same as the MINI rotors). TCE markets a variation of that kit with a 1” thick rotor, which I have gone to because of the level of braking required at Watkins Glen. For that track, I run the 12.2” rotors and 17” wheels to maximize brake size and cooling. For short tracks, like Lime Rock Park, I run the 11.75” rotors with my 15” wheels to get the gearing advantage of the smaller wheels and tires, and the reduced unsprung and rotational weight.

If I can find it, I’ll post a link to a picture of my setup.