I did read through those pages, and that is in fact how I arrived at the queue state representation that I posted above. Unfortunately clearing the queue did not help for long: The tasks kept reappearing.
I have, however -through many trials and tribulations- possibly managed to resolve this problem over the weekend: Logging into the GitLab postgres DB, I found a table called container_repositories which contained references to the repos that were used to test the registry feature. After truncating that table, clearing the queued jobs and restarting GitLab (as well as the entire instance for good measure), it seems to have slowly reverted back to normal over the past 24 hours, at least for the time being. I'm gonna keep an eye on it some more, but it's looking like that might've been it.
It's a bit weird that GitLab would keep spinning tasks endlessly like this, but then again it's a massive piece of software, so perhaps this is simply a strange bug in GitLab itself. In any case, the container registry instructions for GitLab integration did not seem to work that well for us as they produce this behavior whenever I try them out (I tried it twice to make sure), so maybe another look at those could be warranted.