I have yet to get my week old SRT-6 on the road let alone the track but my intuition would be the same as others have mentioned. A Miata has a significant weight and handling advantage. But, an SRT-6 will annihilate them on a power to weight ratio. So use the tools at your disposal. Brake hard, use trailing throttle oversteer to initiate the turn in, and finish with the throttle to keep your attitude balance. My 2008 S2000 is much like a Miata (with more power) and I'm pretty sure the SRT-6 would smoke it around a track once I get used to the suspension setup. You need to get comfortable with alternative methods of steering the car.

Also, you mention "stock tires". Would those be the Conti all season tires or the optional Michelin PS2 summer performance tires? If they are the all season Conti's, you're at a huge disadvantage on a track if everyone else is running race tires or extreme performance street tires. Even if your car has the Michelin summer performance tire option, those tires are ~5 years old now and they have 18,000 miles of wear under their belts (pun intended). The rubber has likely hardened. And the design has been surpassed by newer tires. You can make a huge change to the car's grip with a new set of Conti Extreme Contact DW, Dunlop Sport Maxx TT, or Bridgestone RE-11.

You may want to look at an alternative alignment ultimately but that decision likely comes with increased tire wear off the track.