A few remarks:
It's actually "over five centuries" prior to DS9, not 400, that the triumvirate of CC, OO and DC was founded. Or at least the episode "Defiant" has Dukat saying that this system has worked more or less smoothly for that length of time; perhaps it is actually much older, but suffered its last major breakdown around the time of Bismarck.
And if "when the military dictatorship actually began" might be debatable in the Trek universe, the very idea of whether there existed a military dictatorship on Cardassia at all is less than clear as well. Sure, Central Command had the ability to conduct military operations pretty much as it pleased. But the Detapa Council still apparently had plenty of power, and episodes like "Cardassians" indicate that Central Command had to yield to it and withdraw from Bajor after suffering too many humiliating defeats. (Of course, "Cardassians" did not yet use that exact terminology, but it was still a case of the civilians telling the military to get out of Bajor.)
Except there is evidence that Cardassia is a military dictatorship, Picard's line about the military taking power wouldn't make much sense if Cardassia is not a military dictatorship. Also what was the point of the Cardassian Underground Movement, if Cardassia wasn't a military dictatorship, they even said their purpose was to cause a revolution that would take power away from the military. Heck, in the beginning of season of 4 of DS9, there was a revolution that overthrew the Central Command and gave power to the civilian government, clearly Cardassia would need would need to be a military dictatorship to make sense.
Really what evidence is there that Cardassia isn't a military dictatorship? It was Gul Dukat who said that all 3 bodies function interdependently from one another and he is not the most trust worthy source. And in the episode "The Cardassians" it was said that no civilian official can over rule a decision made by a military official, that military officials ultimately have final say on all major policy decisions.
It seems more likely that the occupation of Bajor was becoming less popular on Cardassia and even some military officials thought it should end, even a dictatorship has to be mindful of public opinion or else they can have a revolution on their hands.
Besides many dictatorships try to appear legitimate by having the trappings of democracy, how many dictatorships have had the title "Democratic Republic" their name or have show elections to justify their rule. It seems likely the the Detapa Council was a glorified debating council, allowed to exist to give the regime some legitimacy, but having no real power.