[bobski]

Maybe pull out the crappy one, grind out any adhesive or material might be in the channel (?) - lay in some kind of adhesive and press it in? Possible, right?
what kind of adhesive would I use?

The with-windshield-replacement molding has the metal reinforcements in it like the original. Getting that molding out without damaging the glass or the frame will be tricky - the rubber hardens, making the instructions in the FSM nigh impossible.
Windo-Weld is good for auto glass, but buying a whole tube to tack in the molding is an expensive solution. Maybe weatherstrip adhesive (3M 08008)?