If you haven't already removed the headliner consider placing something like a thin bed sheet on the top of the dash, especially on top of the instrument cluster. The headliner board can scratch the soft rubber trim around the top of the instrument cluster when attempting to wrestle it out of the vehicle.

I replaced my headliner last year but was not able to smooth out a few wrinkles near the edges and wsa not satisfied with the result. I plan to remove and redo sometime this summer. I think I would have been better off if I trimmed the width of the material close to the size of the board before gluing. I hade a little too much extra material overhanging the edges making it more difficult to get the material to conform to the curves along the edges and corners of the board. The middle of the headliner actually came out looking nice, but once I had a couple wrinkles that I could not get out as the adhesive was starting to bond the materials together there was nothing I could do without deforming or crushing the foam lining. At that point I just made sure everything was sufficiently glued so that the liner wouldn't fall and then hastily trimmed off the extra fabric and reinstalled. I try not to look up at it but most people would probably think that it wasn't that bad. I also plan to set up a more suitable work surface the next time.

I useed 1/8" titanium colored "flat knit" material that I purchased here:

Flat Knit Headliner

The high temp spray adhesive they sell seems to hold up great so far. I'll be buying another couple yards and a can of adhesive in the near future.

For anyone that is considering replacing their falling headliner, the "flat knit" material is the european style fabric that is more of a textured pattern fabric unlike the fuzzy headliner material that was typically installed in domestic models until recently. The titanium colored fabric I've linked to above matched the original headliner fabric very closely. My local JoAnn Fabrics only carries the fuzzy style.