Update from the call centre: after some fast-talking I was able to get that nothing has yet been sent for my DM/COPR. This agent was more policy-bound than the one last week, so my script then was still useful but not quite sufficient.
The agent was under the impression that the eCas status for an outland application would update from "the office will contact you regarding this decision" to "we sent you correspondence on <date> about this decision." As far as I am aware, this is entirely false for outland applicants, although I wish very much it were true.