There was peace under the Empire. The Rebels caused the war and deaths of many. When the Empire took over it mainly affected the Jedi who take away many things from people; such as love, free will, and all emotions. The Dark Side believes in using unlimited power and emotion to overcome your enemy. Besides just because the Emperor and Darth Vader die doesn't mean its the end of the Empire. The Empire lives on long after they're dead. Its an immovable object. The Rebels have done basically... nothing.
It's extremely difficult to call the conditions under the Empire, "peace". What condition existed was tyranny. Dictatorship. I would question the "conservative credentials" of anyone who would side with the Empire, because of what the Empire stood for, and what it took away from it's citizens. Emperor Palpatine in many ways is no different that Chairman MaObama. Rule by executive order. Sidestep the process whenever you can. Consolidate power, while stripping it from the electorate. Oh, and let's not forget the Sith, and their affinity for slavery. Not exactly an ideal which coincides with traditional conservative beliefs.
As for your assertion to the longevity of the Empire, it's a stretch to say the Empire continued on, even after the death of the Emperor. What was left was the Imperial Remnant, which was the holdings of the Empire which the Rebels did not control, or were so remote, the Rebels didn't care about them. The fleet was scattered, under various commands until the emergence of Thrawn. Even Thrawn could not restore the Empire to the power and territory it formerly held under Palpatine, and the Remnant had no choice but to recognize the Republic upon it's reformation.
While the Rebels brought the war, their actions were no different than those of our Founding Fathers, rebelling against oppressive tyranny. Never forget that the Tree of Liberty must be replenished from time to time with the blood of patriots and tyrants...even in a galaxy far far away.