I have been having what feels like driveline slack, with the car seeming to hesitate when responding to the accelerator, as well as a soft but noticeable 'clunk' I can feel when going from D to R, or R to D.

I recently changed out the transmission mount, which SEEMED to improve the problem immensely.. for 1-2 days. Now it feels the same but perhaps a little less noticeable. I still feel vibrations when the transmission is in gear, versus no vibrations when in neutral.

My engine shifts an inch or two when I shift in a stopped position. Transmission shifting is smooth on the highway.

What's the next step? Engine mounts? Or does this indicate some other problem?

 

To Usedname in #1 above:
Worn motor mounts can be checked visually.
1.Open the hood.
2. Start the car.
3. While sitting in the front seat,
keep your foot on the break.
4. Shift into Drive - observe the engine
(thru the front window’s space between
the rear edge of the hood and the top of
the front dash board).
5. Does one side of the engine raise up
excessively?
6. Shift into Reverse. Check if engine
moves, per #5 above.
7. Excessive movement can mean
Worn Motor Mounts.

(I am not a mechanic. This is a simple
preliminary check.)

 

Sounds like motor mounts are worn,
from your description.
(I am unable to delete #2 !)

 

Lord I hope that's the problem and this is fixed. Going to order motor mounts. This only started after an episode of very hard braking to avoid colliding into some idiot who failed to yield.