OK, got it to work after a little mucking around. Here is what I did:
Deleted the Global Tag Blog
Removed the sitewide-tags.php file from within the folder it came in.
Added the sitewide-tags.php to the mu-plugins folder.
All is good so far!
Joss, it looks like you may have the plugin working now. Is that true? In any case, one reason I created a new instance of wpmu was so I could install the site-wide tag plugin before any new blogs were created. Still no luck for me.