Zero vibration in any gear, at any speed....
mmoretti;
This is a shot in the dark,hard to assess a situation without testing, but here goes...the symptom you describe usually relates to the shift fork/ planetary lock in the trans...when you stop and hit park OR any other gear while on ANY degree of a grade, you are essentially putting the entire car's weight on the trans lock out ( this is why it IS recommended in the owners manual to use the hand (electronic) brake).... This will never happen on a manual trans because of the counter rotation of the input shaft and clutch disengagement ....you can still be rolling back and still slide into first;let the clutch out and it fully engages.
Auto trans work quite differently, try the hand brake BEFORE you place it in park,OR drive before the weight of the car rests on the shift fork....that "clunk" you get is actually wearing the shift fork lock tab down rapidly....just a suggestion.
If I stop on an incline at my house to say, check the mail, and put it in "P"...when I get back in, if the hand brake was NOT activated BEFORE I placed it in park....it clunks pretty hard to release the lock, regardless of weather I was going uphill OR downhill,the effect is the same!
Your description points to this phenomena... Activating the hand brake takes the load of the entire car on the locked brakes, rather than on the trans shift fork lock! ..... try it out!