I think we need a little more information about the setup pre- and post-new server and what you did after installing the new server.
Jeremy, I hope this is enough detail. The old server was named "Smythe" and had a net capacity of 6TB. It was running Windows 2008R2 and was also a dc. The new server is named "Synology1812", and it has a net capacity of 16TB, and is, as you would expect, running the Synology OS. With LR not running, I joined the new server to the domain, and copied over all the files and directories from the old server, doing a CRC check on each file to assure integrity. Then I set up the shares on the new server, with the same names and permissions as on the old. I deleted all the files from the old server, and ran a random-write program on the disks containing the old information. Then I ran dcpromo on the old server, and stripped it of all its dc roles. Then I powered it down and gave it away. I pointed the backup scripts at the new server, and I kept two sets of backups from the old server in case I had screwed something up. I verified access to the files on the new server from all workstations.
Then I started Lightroom on a workstation. As expected, it couldn't find the files that had been moved. I right-clicked on every folder that pointed to the old server, and pointed LR to the same folder on the new server. When I was done, I had two instances of the top-level server entities (I don't know what to call them), differing in case. I didn't notice when that happened, but I suspect it had something to do with my typing in the network path in the text entry field sometimes and clicking through the icons sometimes.
Notice that somehow, a similar thing happened to the D: drive, although there are no case differences that I can see there.
For completeness, although I can't figure out how it could affect things, Smythe had a fixed IP address not in the DHCP scope hard-coded into it, and Synology1812 has a fixed IP address achieved through a DHCP reservation that uses the MAC address of the new server to identify it. DHCP is through the Windows Server 2008R2 DHCP program running on one of the dc's and communicating with Active Directory to make all the names consistent.
You might well ask, "Why not rename the new server to the same name as the old server, so Lightroom could find all the folders without any intervention?" I have found that Windows Domain Controllers get confused when old names are reused, especially if the old name had once belonged to a dc.
Thanks for your help.