Huzzah! Success!
Thanks guys - it was definitely a Mind's Eye Malfunction - I was totally wrong in picturing how it clipped in. It actually came out pretty easy. I did run a thin bead of grease in the groove to ease things next time - thanks for the tip.
I also took some pictures that I'll post later for others to better visualize.
[edit]Pictures added...[/edit]
Here is the "female" part of the clip, which is attached to the windshield.
This is the "male" piece, the cowling, which slides into the groove on the clip attached to the windshield. You can see that there is a slight barb on the tongue. However, once you get it started, it is very easy to remove.
On the passenger side, remove the loose end of the cowling from the rubber weather strip, and slide your fingers behind the cowling, with your knuckles against the windshield. Move your fingers as far across, toward the center of the car, as you can, and when it starts to get tight, pull out with your fingers, perpendicular to the windshield. You may get some assistance from using your other hand underneath the cowling to push at the same time. Once the first bit of the tongue-and-groove is separated, the rest will come easily.
Cheers,
Scott.