Answer
Re-run the Event Wizard, normally only ever run once at initial install, and step through it until reaching its Mail Host prompt. Enter the correct value there, click Next, which prompts you to save, and save it. Then cancel out of the rest of the wizard rather than completing every remaining step. This correctly updates the Mail Host setting without needing to complete the full wizard, and without it being editable as a directly-accessible configuration file the way other settings might be.