In case anyone is experiencing problems with this not working, we've just discovered a possible solution.
We set up the package as per instructions but Sublime still kept opening the ss file as a Lisp type. So, we went into Preferences => Browse Packages => Lisp and opened (using Sublime) the 'Lisp.sublime-setting' file, where we found this line: "extensions": ["lisp", "scm", "ss"]
We deleted the "ss" reference here and then our ss files open correctly as SilverStripe type.
By the way, THANKS Benjamin.