Rear Tires Suddenly Lock Up Going 65

I know where a 69 GTX sits today with the same problem. Last time it hit the 1/4 mile track it got into 3rd gear and locked up both rear wheels and slid to a stop. Driver backed it off the track and drove it up on the trailer.
That was years ago and the car hasn't been driven since. Owner has a Dana 60 rear to put under it but really doesn't know if the rear is the problem.
I've heard of times when a floor shifter combined with a broken left ( bisquit type ) motor support changed gears. From drive to reverse is a stretch though.
Bottom line, I've tagged this thread so when yall figure out where the problem is I can call ronnie and tell him. Good luck :)