I wonder how plausible it might have been to make it an independent nation after WW1 along similar lines to Danzig? It was desired by both Austria and Italy, and IIRC had reasonably substantial populations of each.
Thing is...
-Nobody gave a shit what Austria thought.
-It wasn't actually "ethnically mixed." There was a German bit and an Italian bit, clear as day, and Italy grabbed a subtstantial part of the German pit in order to have a defensible Alpine frontier. Italy is not going to accept the creation of a "state" which will eventually try to join Austria/Germany, possibly dragging the Italian bit, which was a decided minority, along with it.
-There is no strategic need for joint control, Danzig, a city as German as Hamburg, was made into a "state" because Poland needed a port (I, for one, maintain that in the immediate post-war Poland actually did need a secure port: even Stresemann waged trade-war on Poland, of all people). Italy's strategic needs are served by annexing Trento and Bozen, and as noted nobody gives a crap abour Austria's strategic needs.