When the problem's not DNS, what is it? Yes, the date was wrong on the reloaded ESXi server. I'm not sure how it happened, but the date was a couple years behind the present. Nowhere in the logs is there any mention of date issues, certificate expiration, etc. so it was pure chance that I noticed it.
So if anyone ever sees the above hot mess of log entries-- check the basics. DNS and NTP. :-)