I feel a kick from under the driver's seat when I'm about to come to a complete stop.

Pull the drive shaft and grease the inside where it connects . Our trucks have a lot of drive shaft play if dry it can cause these symptoms .

 

I thought it was gonna be Roseanne Roseannadanna

 

The 2nd to 3rd gear on 3rd gens up-shifts VERY quickly when cruising. I’m guessing it does the same on downshifting.

Perhaps that’s what you’re feeling more than others do. My guess is you’re feeling it the most in traffic.

 

Move the kid in the back from the drivers side to the passengers and turn the heat up. That should stop it!

 

Does it feel like the truck is sligthly trying to "jump" forward? Or also described as someone lightly running into your rear bumper at a stoplight, like a grandma behind you let her foot off the brake and gave a love tap?

If so, as others mentioned, may want to grease the slip yoke on the rear driveshaft. Pretty normal for these. Motorcraft XG8 seems popular for the task; some other say moly grease, some others use anti-seize but I'm not a fan of it for this application.

One additional thing I can say: after I removed the crappy stock leaf pack and upgraded to my current Deavers this went away for me. So it's caused by axle wrap, can be partially remedied sometimes by re-greasing the slip yoke, and/or upgrading to a better leaf pack with less wrap. Just my $2 dollar bill.

 

Thank you all for your answers, next week I will start with axles wrapping!