One other thing I thought of.
Check the center bracket/bushing that holds the sway bar to the cradle. Try squirting some WD40 into the rubber where it wraps around the bar. It could be binding & popping inside there.

I've never heard of this happening (yet), but I also wonder if the sway bar itself could be fractured. I've seen stranger things.

Thanks guys for all of your suggestions. Finally found and corrected the "PoP". It was the bushings in the engine cradel. Three of the rubber bushings were bad. I had already checked the tightness of them all, and they were as tight as you can get them. You couldn't see any movement. But, when you started, the torque of the engine would pop the cradel. Thanks "Thin Indian" for your suggestion. It corrected it. All of the help is greatly appreciated!

Yes mine does the same thing with slow left turns, how much did it cost you to fix the issue?