I just went out and looked at ours. There is a bracket only on one end of mine, the end in the middle of the windshield. The other end on both is butted up against the wall. I see the end caps you are talking about. A screw holding it up with a flimsy slot for easy installation. About the only thing for a work around is go to a shade guy and see if he has anything similar. Or maybe try gluing the parts back together.
Ours has fallen twice. Both times caused by the bolt in the center of the scissor arms coming loose, and having the nut fall off. I finally redid all of that assembly and used some loctite. When ours came down, the sleeve that goes between the scissor arms fell off too, along with the bushings. Had to search around the cockpit, but finally found all of the pieces.
Good luck.
Stan