You need to use long plastic pry bars, preferably where the tip is split like a 'Y' and bent for a pry angle so it applies pressure to either side of the clip. Saw a long metal one that looked like a BBQ fork... wish I had that one. Those 'A' pillars are particularly nasty. The clips at the front bottom are close together and the panel is wedged in the crack between the metal pillar and the dashboard so it needs to pivot to the center of the windshield to be extracted.
The piece you removed is the overhead 'B' pillar trim panel.
I'd start at the rear, and work one clip at a time to the front. Pull down the 'C' pillar at the 'B' pillar join (back of the door) enough to be able to get at the end of the 'A' pillar. Use a prybar or fingers at both sides of the clips or you'll crack the 'C' pillar where it narrows, where the other clips are. Then work the 'A' pillar trim (above the door) to the front. Use something for a prybar that is long and w/o sharp edges to avoid pressure points - that will crack the face of the plastic. I pulled mine off by hand, but broke a couple of clips. There's some good photos in the newsgroups.
What actually happens is the metal clips get stiff and don't flex as easily any more. Which strains the plastic retainers which have become more brittle.
If yours is a south California car, the plastic panels have been 'baking' in the sun/heat for ~20 years, so the ABS plastic will be brittle. Take time and lots of patience - walk away for a while if you have to. When using JB Weld, apply liberally for a thicker wider bonding surface. I used a similar two-stage product from 'Permatex' and applied to the underside of the cracked plastic panel. Never bothered to repair the clips - the clip mounts shattered and I only broke a couple. Worked great - but I was also gentle with putting it back in. The repair on the overhead 'B' panel was perfect as this is where I started and was finding out how the clips worked (DUH!!).
BTW - You can still buy replacement metal clips if you lost any. Saw them on EBay and someone here posted a part number.
I had previous damage to repair as well when the installers for the previous owners dropped the headliner
to install a Nav system and a TV tuner w/ screen. Had 8 antenna wires installed between the headliner and roof. I removed the lot when redoing the headliner. Look up my headliner tread.