Just a quick update.
First, I disabled, deleted, reinstalled and reconfigured the WP-Discourse plugin. The problem persisted. Posts only made it to Discourse after hitting “Update,” not upon first publishing the post.
Second, I disabled all plugins, re-enabled only the WP-Discourse plugin, and confirmed that posting works properly right away on hitting “Publish.”
Third, I added just Social Warfare to the mix and the problem did not return. This is contrary to my previous results where I confirmed that the conflict was Social Warfare (using just the same method listed here, but without the first step). So I proceeded to further testing, re-enabling all the plugins a few at a time and testing each step of the way. The problem never returned.
Perhaps it has to do with the order that the plugins are enabled? Perhaps it was fixed by a recent update to one of the plugins? (But neither WP-Discourse nor Social Warfare have been recently updated.) So whatever the problem was, it seems to be gone. If it returns I’ll post back in here.