Originals were usually attached across the top edge with about 4 phosphate flat washer head screws. These are installed before the painted moldings.
Also, on a '68, there is normally a notch in the dash pad around the VIN plate.
It's fine to install the dash pad before or after the front glass goes in. On 67-68, I prefer to do it before glass as it's easier to install those screws that go in first. I'm not sure if all cars got those, but I've had original pads that had the extra holes in the pad. Check to see if your car has extra holes across the front in the metal that don't line up with the painted strip screws.
Haven't seen a speaker section collapse like that. I always store dash pads top facing down on a flat surface.
Original dash pads should have a dull/satin finish.