Rear window leakage/71 MachI

[JavelinJethro]

I have a question for anyone who might have a solution: On a 71-73 Sportsroof (and coupe) the headliner wraps over and glues to the metal lip of the rear window opening. The ribbon sealer for the glass lays on top of this wrapped over headliner and seals to the headliner material itself. I think that water would run down between the headliner and the metal lip and therefore leak. I'm of the opinion that this is a poor design, but I am at a loss as to how to proceed. I'm about ready to drop the back glass in this 71 Mach I, but I'm somehow convinced that this window is going to leak unless something is done. Anyone dealt with this before, or have a solution?