6 speed transmission, weird behavior.

[autoque]

Most noticeable when I'm doing the parking maneuver, sometimes when I shift between drive reverse or park, the car suddenly gains momentum to go forward as if something has bumped into the vehicle and is pushing it from behind. It's sort of like shifting into gear when the engine's rpm is higher than the idle rpm. And it's also like shifting into park on an incline without the sidebrake. Even on a perfectly flat surface, after shifting into Park the car somehow still has the momentum to go forward and after I let go of the brakes, I can feel the parking pawl resisting the car from going forward as the car's nose dips moderately. If put in Neutral and let go of the brakes, the car rolls forward upto 3 feet. How I know this is about to happen is when I shift into Drive, I feel more than usual load from the brake pedal and it's exactly when I know the transmission is misbehaving and shifting into Park or Neutral will result in what's described above. It doesn't happen all the time, but when it does it's pretty annoying.
All of this started after the transmission replacement. Any idea?