Does the Bible permit Christians to go outside the established political process to change or overthrow their government?
A: I think your conclusions are biblical. Yes, we are told to obey the established laws of the land in which we live. Yes, there are biblical precedents for what we call "civil disobedience" for any time the government may establish a law or ordinance that would seek to render ineffective our obedience to God's Word. For example, if our nation ever went so far as to declare that evangelizing was illegal, those of us who take God's Word seriously would have to say, “Whether it is right in the sight of God to listen to you rather than to God, you must judge, for we cannot but speak of what we have seen and heard.” Acts 4:19-20 (ESV) And we would say this because we have already received an explicit directive from our Lord to go into all the world and make disciples of all nations. (Matthew 28) That directive trumps any contradictory edict or law of man that might compel us to obey.
As far as "overthrowing the government" goes, I'm not sure the American Revolution entirely qualifies as a genuine government overthrow. I know the American colonists were attempting to gain their independence from British rule here in America, but as far as I know they never took their battle to Britain in any attempt to unseat the Monarchy or overthrow the government there. They seemed content to let England function with whatever authority they saw fit. They simply wanted the British to leave them alone to live in the Americas with a new Constitution and new freedoms. What we're really asking is whether there is biblical grounds for a political separatist movement when we feel our rights and religious freedoms are being violated.
Therefore, I would not be comfortable with anyone using God's Word to justify or substantiate any type of government overthrow. Much of the New Testament was written during times of oppressive and dictatorial leaders and governing bodies, and still the Apostles and writers of the New Testament refrained from using any language that would encourage believers to put their energy toward any kind of government coup or illegal government reform. In fact, we are reminded in God's Word that our true citizenship is in heaven. (Philippians 3:20) As for participating in something like the American Revolution, I believe it would be up to the conscience of each individual before God. Looking back, I would have to say I'm personally glad those early Americans did what they did.