This website of Reformed Calvinists is useful in that it evinces a remnant of Calvinist covenanters who never accepted the principles of republicanism or American constitutionalism. They have just as strong a claim if not stronger to the heritage of Luther, to Calvin, to Rutherford, and so and and so forth. Here is how they trace their heritage of authors:
John Brown, of Wamphray.
John McMillan I.
John McMillan II.
John McMillan III.
James R. Willson.
William L. Roberts.
James M. Willson.
James F. Fulton.
T. James Blair.
John Witherspoon helped to get many Americans on board with Revolution and the Constitution. However, he did so in large part by positing non-Calvinist, non-Christian Lockean and Scottish Enlightenment principles from the pulpit.
Samuel Rutherford of "Lex Rex" fame may have been useful for revolution. But on matters of unalienable natural rights of conscience -- something key to American natural rights republican theory -- he would have been diametrically opposed to what America's Founders stood for. Here is a blurb from their site where Rutherford approves of Calvin's execution of Servetus simply for publicly denying the Trinity:
"It was justice, not cruelty, yea mercy to the Church of God, to take away the life of Servetus, who used such spirituall and diabolick cruelty to many thousand soules, whom he did pervert, and by his Booke, does yet lead into perdition."
—Samuel Rutherfurd, A Free Disputation Against Pretended Liberty of Conscience. (1649).
The whole page gives a plethora of writings showing the logic of why Calvinist Christians ought not tolerate other religions, or heresies within the Christian religion. Their logic is strong -- if false religions and heresies damn souls for eternity, well then what can be more important than shutting their mouths. This is the polar opposite of Jefferson's notion that it does me no injury for my neighbor to say there are no gods or twenty gods.... On the other hand America's Founders did realize that if we followed Calvin's or Rutherford's logic in this regard, you get a lot of bloodshed. Tolerance and then recognizing the full unalienable rights of conscience at the very least, avoids that.