Thanks! An alternate idea is to eschew Scheduled Posts and use the Discourse Automation (see Discourse Automation - #109 by mattdm). But that automation script doesn’t exist (yet?) — and while more flexible, seems more hacky than the normal schedule-post workflow.
(As a slightly confused aside: I know that trust level does affect some of the things on that menu — it shows for TL4 users but they don’t have all the options that mods have, and there’s a category moderator / full moderator distinction too. So there’s something granular somewhere…)