There are basically five layers to a headliner. The substrate, glue, foam, glue and cloth. In older cars when the cloth starts to fall down, its not the glue that has failed, it is the foam that has started to deteriorate and break down into dust. Removing the old cloth from the substrate is easy. The trick is getting all the glue with bits of foam in it off the substrate. I have used a wire wheel on a drill to do this with success, but you have to be careful not to dig in too far and damage the substrate. I think I have seen the write up on the other site you reference, and it is a very good one. I forget if they include this or not, but the trick to gluing new cloth to the substrate is to build a wood frame that holds the cloth and inch or so off the substrate. With the frame on the floor next to the substrate, staple the cloth to the frame, spray glue on the substrate, place the frame over the substrate, and then press the cloth down to contact the glue starting in the middle and working your way out. Once that is done, trim the cloth around the substrate leaving about 1" of cloth hanging over the edge. Turn the substrate over, and working in 1' sections put glue on the back side edge of the substrate, fold the cloth over, and use clothes pins to clamp the cloth in place until the glue cures. Like I said, work in 1' sections as you work your way around the perimeter.
Pictures of the different steps as you do it would be very helpful to the forum.
2001 Bonneville SSEi (retired at 365,000 Kms.)
2014 Jeep Grand Cherokee Overland (yes, I know its not a GM)