Mine acted just like that for quite a while. It would go down the track straight (pretty much anyway) - then when you backed out of the throttle it would get seriously upset. I thought it was my tires or something - but took a pass on street tires and it still did it. Everything appeared tight and didn't look like anything had moved. I measured it and the rearend was out of square. I'm on leaf springs and it actually ripped the locater hole in the spring pad to move itself out of square. It was off by 1/4".

Once I got it all squared-up it drove fine again.

It won't cost anything to put a tape on it. Have somebody help you measure diagonally from corner to corner, and if it's off it will show up quickly.