Why not clean the glass thoroughly in that spot, front and rear, cut a piece of 3/8-inch glass the exact length needed and a couple inches wide, and silicone it in place? You'd need to have a bar clamp on hand to apply just enough pressure to counteract the bowing while the silicone cures. Once that's done, you will have a brace that is far stronger than that flimsy piece of plastic ever was.
If you carefully cut out the trim piece from where this is done, the repair will be quite acceptable in appearance. It will be strongest if you cut the brace long enough so that it sits on top of the front and rear panes, rather than trying to sandwich it in between them.