Let those states that wish to leave secede from the United States
http://www.thepetitionsite.com/228/644/059/let-those-states-that-wish-to-leave-seceed-from-the-united-states/
Maybe have a national referendum first.
If those who want to secede outnumber those that don't, give those who want to secede a choice to stay and preserve the union, mandating that other state and federal employees and elected officials re-constitute our constitutional Republic or hit the road, Jack, and don'tcha come back no mo'.
Then we start over with a clean slate, eliminating all the non-constitutional laws, treaties, executive orders, etc., and all infringements.
I think that would be fulfilling the requirement of the states who want to petition for new federal and state officials without destroying the infra-structure and insuring continuity of government.
That would leave our constitutional Republic intact without spilling a whole lot of blood.