Did you ever have a soft top installed? Do I understand that you have an OE frame and an aftermarket top on it? That cold be the issue. Maybe you need to flex the bows up to add some tension?
I doubt anything stretched while in the box. If anything, the opposite would happen.
Yes to the top inflating. Mine lifts up off the front bow once I get up to speed. The rear windows do the opposite... they get sucked in creating even more tension on the bottom tabs.. no way they are coming out.
Never heard of King top.
One of two things happening here..
Either there is something up under the lip of the tub rail that is preventing the plastic tabs on the bottom of the window from seating all the way up under the belt rail or there is a kink in the plastic tab on the window that is preventing it from sitting all the way up.
I can tell you this... when I install my side windows there is quite a bit of tension on them when the tabs are being inserted. Sometimes the bottom edge doesn't seat all the up and under the belt rail and it needs a gentle tap with the heel of my hand, then it sits flat and fully inserted. Once in, there is no way it is coming out without unzipping the window.
Another thought.. if the plastic tab on the window is designed in multiple sections, maybe one section is in but another isn't?