Well I guess you know better than I do what is possible for you and what isn't.
I can't think of any other solution. After all, you have a polity that you equate with freedom and democracy and a government that you can't control. It seems to me that you have to change either your government or your ideology.
Russia managed to de-ideologize its state, going backwards rather than what everyone had thought was "forwards".
And after all, the people pushing for a North American Union are trying to fuse together a monarchy and a republic. And many countries in the Commonwealth ARE republics, and some of them now are not even former British colonies.
But there is no point in flogging a dead horse and after all it is a problem for you to solve not me.