Class was ESP and I was on 295/40/18 A6s. I'll try and track down some pics of the car from this past weekend and see if I see anything. But I was thinking spring rate and less roll was the answer, but I wasn't 100% sure. Guess I'll be saving up for some coils while I get more seat time this year lol
ohhh.... my bad. The pic in your sig is a little out of date, I guess.

That's a decent sized tire for ESP, of course, but even a bone stock 5.0 makes 380whp - which is a lot for two of those on the drive axle when used in a low speed parking lot event. As I've said many times before, you can never have TOO much tire on these cars, especially when you start adding more power...
This picture above was during a (failed) experiment back in 2012, when we were still running ESP. Front was the same 18x11"/315mm A6 but the rear had the 18x12" wheel and 345/35/18 Hoosier A6. Brand new, for this event. Sealed asphalt lot, and that power oversteer condition was in a medium speed 2nd gear corner, with 430 whp (2 bolt-ons + a tune). Granted, this was before we did the Watts, the Torsen T-2R, and later the LCAs and relocation brackets after we left ESP, but it was still
rear traction limited in autocross events. With a 13.2" wide tread width Hoosier A6.
We went back to a 315mm tire because of tire rub issues on the rear, with the 345mm tire. But on a
serious ESP effort with one of these S197 cars, I definitely would build the car around this rear tire. Cut the fenders, flare for clearance, etc. And I'd run an almost matching 335mm front. We didn't get that far before we left ESP class, but that's the magic set-up. Every time we've added tire width to this car it 1) got faster and 2) easier to drive.
Not everyone is willing to cut up a new or nearly new $30-45K 2011-2014 Mustang GT/Boss302, so in that case go with the widest that can fit under the stock fenders (315mm) and make the mods necessary to fit that. The 295/40/18 was on close-out for almost 1/3rd the normal cost, so that was a no-brainer. But don't expect it to make the grip of the 315... or the 335... or the 345mm A6.
As for suspension mods... sure, with even the 295 A6 you're probably overtaxing the shocks and lowering springs you have. We had 450#/in front and 175 #/in rear springs on Moton Motorsport 2-way coilovers at the 2012 Nats (above and below) and look at how much bodyroll and brake dive we still had. I've gone to 600#/in fronts and 250 #/in rears (which works great on track) but
still have a lot of bodyroll in autocross events. With huge swaybars at nearly full stiff, too.
Autocross S197 Mustangs in ESP really need... ludicrous tires, and ridiculous spring rates.