The full story is that I applied an update to this NAS just before this foolishness, so I have every reason to believe that is the culprit, but even knowing this, I am unable to diagnose the problem. Especially given that only one domain name has a problem -- "NAS0.TCLC.org". It is clearly the domain name, not the device; a different domain name (NASX.TCLC.org) works just fine. And the same domain name fails regardless of the IP.
'arp -a', look ok? Should clear at reboot but I've seen stranger things. Is there anything in hosts besides localhost entries? Does the output of the hostname command match the address record? nslookup the address of your machine and see if it's the only entry for it, is this the only interface live?
When I first started to investigate this, I found a bogus DNS entry defining NAS0.TCLC.org as 10.1.1.103 and DHCP told me that this was the address of ASUSTOR-3204T.TCLC.org, which, as you can guess, turned out to be the NAS. I deleted this and cleaned up DNS and DHCP and I have eradicated 10.1.1.103 from the system. I also have no reason why the NAS was asking for an IP. I'm going to chalk it up to some sort of update semantics, because the NAS is configured with a static IP and a DHCP reservation.
All of your proposed diagnostics return exactly what you would expect. arp, nbtstat, nslookup, ping, ... I have even disjoined and rejoined the domain. So far, nothing has had any effect.
From windows PowerShell on any windows machine in the domain: