Caesar was much more tyrannical than George III ever thought of being and Jesus, Paul and the Apostles never called for revolution, to the contrary they said give to Caesar what is Caesars. They only opposed Caesar where it was in direct conflict with God’s command.
One principle that the Founding Fathers were familiar with was the theory of the lesser magistrate. The background is that the governments of the 13 colonies declared resistance to the infringements on liberties that the British Crown wanted to impose. The colonial militias were not an armed rabble like the so called militia groups of today. They were organized at the local level by county or town authorities and governed by the colonial governments. The Declaration of Independence was signed by representatives of the 13 colonies who were duly appointed to the Continental Congress by the provincial legislatures. Those legislatures and their governors were the lesser magistrates who saw their duty as protecting the rights of Englishmen that the Crown sought to abrogate.
The War for Independence was not contrary to Romans 13, as the soldiers were obedient to the commands of the provincial/state authorities that were duly constituted.