Aha! This problem is resolved by choosing the "System Default" option under Settings > Audio > Advanced Tweaks > Volume Levels. Mine had been set to 30.
Thanks very much to Geiler Heinz in this post:
I think this must be a bug (and if it can't be fixed, please add a comment on the Volume Levels screen explaining that choosing a value other than System Default will cause the Chromecast problem). I liked the higher granularity. (Although while the System Default setting is normally 16 volume increments, I get about 49 increments (each increment is 2 or 3%) when I'm using Chromecast. Which is great, but I'd like to still have the higher granularity when not using Chromecast.)