Thanks for the advice everybody. I could have spent several hours poking around inside my Model 29 today, but instead I took it to a local gunsmith with a great Yelp reputation. Upon hearing the symptoms, he surmised that it probably needed a cylinder stop spring and perhaps some fitting. (He will have it fixed in a couple of weeks. I will report back about what he found and how well his efforts paid off).

Then I went to the range and spent all afternoon shooting.