Thanks, everyone, for your help. I started this post saying LS1200, but in fact I have a TS1200. Correct facts help!
In my spare time, I've been continuing to work on this. Still no success, but I can now be more precise on where I am:
Point 1: I do general network admin using a Mac. Buffalo offers a firmware updater for the Mac, but it doesn't include the DEBUG feature that the Windows version has.
Point 2: I got the firmware updater running on a Windows machine on our network, with an edited .ini file with VersionCheck off and Debug on.
Point 3: With everything checked in the Debug Mode panel except Rebuild Partition Table, I successfully updated my TS1200,
Point 4: After the reboot completed, access to the GUI still fails in the same way.
Point 5: Using Netscape Debug mode, it shows the JavaScript failing because Ext.globalValues.nasFeature["REGION_CODE"] is null.
Point 6: It looks like the GUI is failing because there is clobbered data somewhere that is not restored by the firmware updater.
Point 7: The only unchecked box in the Debug Mode Panel is Rebuild Partition Table, but that seems unrelated to the missing JavaScript data.
So, if you're still with me at this point and have any thoughts or suggestions, they would be much appreciated!!