Fantastic so Milan could become the "Ambrosian Republic"!
It will be merely a change of government or we the country change tag, too?
It should not have the Duky's flag but this flag to be historically correct:
Do you talk of a "special" type of Republic... how is this special?
Talking of the Republican Tradition is this affects Noble Republic, too?
In my opinion those are Republic only by name they elect a monarch, not an "official" of some sort... on the other hand "legitimacy" could not be correct in any way as we don't have a dynasty and the "King" is elected by the nobles so it is legitimated by them.
Maybe we could think the nobles could dethrone him in some circumstances or, on other hand, he could become so powerful to become really a "King" (the government changes to Monarchy).
P.S. I continue to have the doubt that Noble Republic elected its "King" any 4 years, is this really correct? The King of Poland (and after of the Commonwealth) was elected any 4 years of he was King for life? I suppose the latter...