Had a new transmission put in about 2 weeks ago now, and I've got two things I believe are not related.

1. If I drive under power and come to a stop that isn't a rolling glide in stop, I put my foot on the brake and stop completely and wait 2-3 seconds I get a weird clunk that repeats 2-3 times and almost makes the vehicle move. At first it felt like brake failure...but it feels like it's coming from the rear and it's hard to repeat on demand. I brought it to Chevy and of course the ghost was out to lunch


2. Clunk leaving from a stop seems to not be related as this is a heavier clunk. I can count to two for this one...but again...random and loudness varies.

 

I'm not an expert but what you described sounds almost like loose tranny or motor mounts.
The clunk when you start moving could be the tranny or motor shifting backwards, then when you stop, it shifts forward giving a nice CLUNK

 

The first one is definitely power related...I had a non expert in the vehicle who said something along the lines of torque converter.

The second one is def in the rear.