I take it you're in Lansing, MI.???? Do you have any circle burner buddies up there that would let you get some scale time? A good set of 4 wheel scales will tell you a lot about how the suspension is "loaded". Wish you lived closer, almost sounds to me like something is loading up one side or the other on the car when you launch. Could be mis-matched springs or the shocks themselves.....Does the car always move the same direction when you launch or ? You could also try moving the shocks and springs from side to side on the rear, see which way the car moves then......

I had a similar deal many moons back.....Turned out to be a pin hole in a tranny cooler line that would spray a fine mist of fluid in front of the right rear tire!!!!