Sky - Something is definitely wrong with your car. The inconsistency makes me wonder about the computer (a la Unit) or electrical. Hell, maybe you just need a complete tune-up?
Concerning your experience on the slicks...I had the exact same thing happen to me once. At the track on borrowed slicks with around 9 psi in them. I dropped the clutch at 4000 and couldn't believe the feeling. I had a 1.7x 60' time, deep into the 12's for sure...then as I'm getting to the top of second the back end starts moving back and forth. Not much at first, but it kept getting worse. By middle of 3rd I thought I was going to put her in the wall!
The back end was uncontrollable. I slowed down in a controled manner and coasted throught the traps.
As soon as I got back to the pits, I swapped the slicks for my drag radials and watched the rest of the night. I firmly believe that there wasn't enough pressure in the slicks, but the guy that let me borrow them insisted that 9 psi was perfect???
Good luck with finding the "bugs" in your car and keep us posted.
E