I did another windscreen today for a friend. This time I used a stiff one-inch putty knife (as suggested in the directions I prepared) to separate the two gray plastic pieces in the stock mechanism. It worked like a charm: I had it apart in a few minutes.

For those of you who will be taking apart the mechanism to install my new screen, I strongly recommend this approach.

As noted in another post, when you pry apart the base, you'll hear cracking sounds. Don't worry, it's just the glue separating.