Update:
Sadly, Canvas doesn't fail to disappoint. My "stale" announcements just went out today, a week after the course end date. It also let me delete one that still remained delayed until later today, luckily, because had the course become read-only, this last announcement would have also gone out without giving me an ability to intervene.
@nuscitpkg, this should be a welcome news for your institution - it appears that the current Canvas version allows you to communicate with students after the course end date with no issues.
As far as the workaround for my problem, I guess what I can do is delay them until after the next semester starts (e.g., a year out), then after the course is copied to the next semester go back and delete them from the old course. That's more busywork and more things to remember to do, but that would do the job.
Thanks everyone for responding!