It works. The 3D-printed part arrived in the mail yesterday and it appears to do the job. Here's a video of it (the white piece that slides around in the center of the mechanism) at work. Later, I'll write a longer description of what I learned in the process of replacing it. And that post will include the CAD file of the part.
Note: I received two copies of the part. You can see the second copy in profile on the counter to the right of the mechanism.
Note: I received two copies of the part. You can see the second copy in profile on the counter to the right of the mechanism.