What it says on the tin: if you make a manual save or quick save during Anarchy (autosaves seem unaffected,) and then load the save, the remaining number of turns of Anarchy will have been decremented by one. You can indeed change your government in a single turn simply by saving and reloading as many times as the game speed requires.

Attached find a vanilla save with the UE ready to change their government to test it yourself.

Anarchy_Bug_Test.sav