It is not your transmission. The culprit is your rear driveshaft Sleeve Yoke, or more commonly referred to as a "Slip Yoke". It's the yoke near the rear differential. The "kick" you're feeling is the sleeve yoke becoming unbound coming to a stop. The sleeve yoke is able to slide on the driveshaft (the FSM calls it a propeller shaft) to allow for the rear suspension movement. The sleeve yoke is compressing, getting a hung up on the splines of the propeller shaft and then unbinding all of a sudden giving you that clunk or bump feeling. When it's really bad, it feels like somebody has rear-ended you.
I had this problem and was able to fix it by greasing my sleeve yoke with a special Ford XG-8 grease somebody on the forum recommended. First try the easiest route by injecting a multipurpose lithium based grease into the sleeve yoke zerk fitting. Pump a good amount into there because a few squirts isn't going to do it. To make sure you didn't overfill it, take a small metric socket, I think it's a 7mm and remove the zerk fitting. Now entertain your neighbors by jumping up and down on the rear bumper to evacuate any excess grease out the zerk fitting hole. Put the zerk fitting back in and drive it around to see if the problem is still there. It might take some time for the grease to make its way to the upper part of the splines.
If your problems persist, take a look at these videos I made of addressing this problem. If you have any questions, ask. I sometimes feel a little bump now and then but nothing like it use to be. I'll probably pull the slip yoke again on my rig because it seems to be the best way to properly lubricate the upper splines of the propeller shaft. Good luck!
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