[FredBMOC]

Tin-man,
As a newbie with some track experience my understanding is that the problem with Cobras and even more so with automatic transmissions is a combination of factors including the short wheel base, heavy engine, and way too much power but regarding the automatic transmission the problem is as follows:
When one changes gears in a car the weight distribution of the car changes and either the back or front end instantaneously becomes heavier depending on what gear shift you did ( up or down ). This is fine as long as you are planning on it and in fact is beneficial: for example you come down a straight, brake in a straight line ( putting more weight on the front end for better braking), downshift ( again putting more weight on the front end for better braking), enter the turn and accelerate through the turn (putting more weight on the rear tires for better traction) and keeping the rear end planted on the ground. All as it should be for spirited and track driving..
Now this same process on an automatic car becomes problematic as you can't really control when the shift occurs: you do as I describe above braking but the car doesn't downshift you come to the turn , slow down, the car is weighted and in balance, now you step on the gas and the car downshifts changing the balance of the car, in quick succession first forward as it downshifts than back as you accelerate. These weight redistribution changes can upset the balance of the vehicle and cause it to go into a spin or simply to have you pointed towards the inside or outside of the turn when you were not really planning on it; not a good situation...
Anyway this is a just a very short and simple explanation of some of the issues faced. Add to that the fact that you have an insane power to ratio and can simply brake traction on the rear wheels any time you twitch your foot on the gas and you have a recipe for a challenging vehicle to drive.

Best wishes with your new ride!

Fred