Just an update (as there is nothing worse than searching for a topic and finding that the answer was never confirmed.)
Moving the dedicated server was a success. Here's the exact process I went through on my Windows 10 machine in case it helps someone else later. This included installing to a different Windows profile name and putting the server on a drive with a different drive letter:
1. I backed up the saves as per the FAQ item (for me it was \AppData\Roaming\7DaysToDie. I backed up the entire folder. I suspect that the relevant folders were \Saves, \SavesLocal, and \GeneratedWorlds. (Note that the FAQ calls it the 'Worlds' folder, which I'm guessing is from an earlier version.)
2. I backed up the installed dedicated server folder (IE - the folder where startdedicated.bat and serverconfig.xml are.) In the end, the only file I actually needed from here was serverconfig.xml. Note that this was in the dedicated server install directory, not the game directory.
3. After the format, I dropped the backed up \AppData\Roaming\7DaysToDie folder into the new \AppData\Roaming\
4. I reinstalled the server via SteamCMD normally, and copied the backed up serverconfig.xml to the new server install directory.
I also had to re-tweak my network settings, but that isn't a 7D2D issue.
Everything is working exactly as it should be. The world is intact, the players are intact, items that were forging are still forging, etc.