I allowed the glue a little over an hour to dry. And then held the tension rod (for lack of a better term) that the shade is wrapped around in place while I rotated the shade to build tension (exactly how the shades that they used to pu t in houses work).
It looks like the plastic being broken was causing the problem. The rod needs to be held in place in a slot -- and when the housing was cracked, that slot was no longer able to hold the tension rod.
I have it installed back in my Jeep now, and the sunshade is opening and closing just fine. Still, I intend to be very careful with it -- if I even open it at all -- because of the repair and because it was vulnerable to breaking in the first place.
Moral of the story: If you are going to allow your drunk adult friends to ride in the backseat, make sure that the sunshades are retracted so they don't get any crazy ideas