Representational democracy long predates the Presbyterians.
And in fact, it was not representational democracy that what the revolutionary aspect of the American republic. It was the concept of inalienable individual rights which was novel. In fact it really had no legitimate precedent in any practical sense, in all of recorded history (although it was advanced theoretically by many upon whose shoulders the American founders stood).
And certainly rights were not a concept thought highly of by the church in ANY sense. And the Bible makes no mention of them whatsoever. The 10 commandments (when considered as codified state law) run diametrically opposed to the concept of rights.
A reasonable apologetic in support of rights can be constructed from the teachings of Jesus of Nazareth (I have done so myself), but I haven't seen it advanced by many Christians.
The concept of "inalienable individual rights" not a belief of Christians or prized by the churches? I disagree. The whole idea behind the Reformation is justification by faith alone - that each individual believer had his own relationship with God without the intercession of priests or bishops. Even more radical was the idea that a believer could read and interpret the Bible for himself. The individualism of modern Western civilization was born in the Reformation (and Renaissance), in which many of the ideas of the Enlightenment are rooted.
The Declaration is quite clear, we are endowed by our Creator "with certain inalienable rights . . . ."