Crikey, I loath PHP. I almost hated it due to an oversight in modifying this site’s scripts.
return “$root/$blog_id”;
The above does, in fact, work. It was getting butchered elsewhere.
Every thumbnailed image in WordPress assumed that I was the only user and knew nothing of the dynamic paths. I’ve since re-written the thumbnail script (cropper.php) to convert /path/ to blog_ids for proper operation and should polish off the results and put them back upstream (if possible).