My '98 Grand Cherokee w/ Quadra Trak has started lurching forward when
in park with the engine off. This is not the problem with the park pin
jumping. Does the same while the engine is running also if in park.

The car has to be hot such as driving a ways on the freeway. My 10
minute commute from home does not warm it up enough. Has to be good
and hot from 20 minutes or so on the freeway.

When hot, pulling into a tight turn feels like one of the differentials
is locking up. Sounds and feels bad. Then, if I park on a level
surface and turn off the engine, after about 5 seconds, the car jumps
forward about 1 inch. 5 seconds later, does it again. It can do this
5 or 8 times. It is a definite accelerating jump, not simply rolling.
It is not rolling down hill because putting it in neutral does not
cause it to roll. Leaving it in park and trying to move it has no
effect.

Fluids are all full.

No bad noises while driving until doing a tight turn, such as pulling
into a parking space. The bad noises are grinding type, more line a
lot of strain on stuff with one of the wheels slipping and some vehicle
lurching. Feels like the rear differential if I had to guess.

The service tech at the local Jeep dealer said he's never seen this in
his 15 years there.

Any ideas?

David