I was watching a YouTube video last night about the Clavinet D6 last night, in which they mentioned the string damping, which seems very similar to the Stick method.

In the video - https://www.youtube.com/watch?v=zGAnyZIGA0I at from about 2m37s - they were using Clavigel, but from the factory they were damped with 3-ply polyester yarn. Have a read here: https://www.clavinet.com/yarn.php

Has anyone ever tried this method with any success?

No but thanks for the fascinating insight.

For his song "Margaritas in the Waves," Emmett would place a peice of cellophane tape over the strings near the bridge. I think he was going for a marimba-type sound, but now that I think about it, it was a bit clavinet-like. He would pull off the tape towards the end song (3:15) to let the strings ring out for the rest of the peice.

Jim Lampi talked a bit about that in his TnT session. He used a damping technique on his album North. I'd be curious to see if that same damper that was used on the NS could be applied to a Chapman Stick?

Yes, at recordings to play with a percussively muted sound, or in some cases achieving "experimental overtones". I add the extra damper objects close to the bridge. From the prepared guitar/piano community I nicked the method of applying paper clips to strings, which allows you to move clips around while playing and change the overtone structure.

I've never used this trick at a concert though, as finding the optimal placement takes more time and precision than a typical audience would accept