This is just the joy of having more-than-sufficient torque available. The diff brace won't really help that. Personally I'm confused about the brace. It's an IRS - it shouldn't matter what the diff does. Maybe with road course racing there's some subtle changes to some cornering behaviors, but I don't know. There's another company that sells high durometer bushings for various Kia IRSes, and I think one other brace manufacturer, so I guess that means there's some truth to it?
Wider and stickier tires help, but they can only take so much. Look for a tire with a treadwear rating around 200. They don't last long.
The JB4 causes the engine to put out much more torque at lower RPMs than the ECU expects, and the traction control can't keep up. The nannies are still pretty easy to work with on this car - the ECU lets you get away with a lot, but still stops you from killing yourself.
This is just a chance to be a better driver.