Proporsche and Gendaito were both correct, but their suggestions didn’t fix the problem, but their thoughts got me on the right path.
One Phillips screw holding the sunroof transmission assembly was loose. But tightening that didn’t fix the slipping problem.
So thinking the pinion gear was worn, I bought a new one, but that didn’t fix it either. There was still the gronk gronk gronk noise and the sunroof wouldn’t lift into place on the right rear, so it actually made things worse.
So I thought the spiral wrap on the cable for the right side must be worn at the point that the sunroof should be lifting into place, causing the disengagement of the pinion. But the cable looked okay.
In studying how the pinion gear is not fully engaging the cable, it occurred to me that the cables may be too far away from the gear, allowing it to slip.
The solution was to use big channel lock pliers to squeeze the metal carrier for the cable housings on either side of the pinion gear socket. This forced the cables closer to the pinion. Now the sunroof works smoothly, quietly, and shuts as it should.
The photos below illustrate the area where the pinion gear nests between the spiral of the cables and you can imagine how the gear would slip if the cables are too far apart.
It is a mystery to my why there was too much clearance, though wear over time would certainly be a contributing factor. Also, my particular part may have been welded up that way from the factory. Another possibility is that since the drive transmission mount screws were loose, which also hold this assembly in place, may have let the thing flex over time spreading the cable carriers apart a bit. It wouldn’t take much clearance to let the pinion gear slip.
Thanks for getting me on the proper trail. Jeff