Since the governing authorities Paul was writing of were the Romans, a far more tyrannical government than King George, yes the signers were rebelling against God. We need to be cautious about assigning our American values and standards over the Scriptures.

“Let everyone be subject to the governing authorities, for there is no authority except that which God has established. The authorities that exist have been established by God. Consequently, whoever rebels against the authority is rebelling against what God has instituted.”

So the signers of the Declaration of Independence were rebelling against God? Should we also condemn in God’s name the revolutionary movements in Tunisia and Egypt? How about the slave masters of the American South? Their authority was established by God?

For the one in authority is God’s servant for your good. But if you do wrong, be afraid, for rulers do not bear the sword for no reason. They are God’s servants, agents of wrath to bring punishment on the wrongdoer. Therefore, it is necessary to submit to the authorities, not only because of possible punishment but also as a matter of conscience.

See also article 6 of the anabaptist (and thus pacifist) Schleitheim Confession:

The sword is an ordering of God outside the perfection of Christ. It punishes and kills the wicked and guards and protects the good. In the law the sword is established over the wicked for punishment and for death and the secular rulers are established to wield the same.

Your point about Solomon is valid. A theocratically elected leader has the right to pronounce a death penalty, just like Peter did in Acts 5:1-10.