I just discovered the /admin/customize/watched_words/action/replace interface, which appears to work for this. Also allows uploading a number of replacements from a .csv file.
The downside is that it requires a rake posts:rebake to make the replacements appear in prior posts, which in my case takes over 24 hours to run. The main purpose of the Watched Words feature appears to be for censoring or otherwise acting on words (or emojis) that appear in new posts, whereas in my case the problem is mainly with old posts where the old forum engine automatically inserted its unique codes when the user added an emoji to a post.