Tied typeglobs exist. But AFAIK, their only purpose is for tying filehandles, nothing else. See the subsection "Tying FileHandles" in perltie. I think you're out of luck.
You can use a blessed typeglob as an object, or at least a reference to one, so you might just try a different interface, not the tied one. See Symbol, and the function gensym().
Comment on Re: Tied hashes and arrays, yeah. But tied typeglobs?