Update: 44 minutes of conversation later: they don't know. The CS Rep (in all fairness, she was pretty smart, unlike my snotty comment above) thinks "system" is a chron job, and it's deleting stuff automatically. She checked and discovered that post #s 8833-8837 were all missing/deleted, and they all dated to March 2015. I checked my audit logs a little more thoroughly, and found that "system" is what shows up when I schedule a post for publication later, and it publishes (in which case, it reads private to published, instead of deleted) She's never seen anything like it before, but vaguely similar issues were raised where it turned out to be a plugin using "system" to automate jobs.
Seems the solution is to deactivate each plugin one at a time, then wait check, as each "system" entry is almost a week apart. If I find an answer, I will post it here.