This clause carries a lot of weight in my opinion.
That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness.
My thinking is that to err on the side of caution, "Just cause" should be left to the eye of the beholder. The English argued that the Colonists really didn't have a good reason for leaving, the stamp acts had been repealed, they were discussing representation in parliament, and most of their grievances were being addressed.
The colonists disagreed that their grievances had been adequately assuaged, and so they invoked their "natural law" right to leave and form their own government.
I will point out to you that the only extant philosopher of natural law that argued the right to independence and the right to form a Free Republic was Emerich de Vattel. No other writer of natural law would have dared suggest such a thing because all the rest of them lived in Monarchies.
Only Vattel, as a citizen of the Kingless Swiss Republic could make such a bold suggestion. The Idea of Independence was put into their heads by Vattel. :)
The DoI was simply not about whether they had a “right” to rebel and, if successful, be independent. It was t show why their rebellion was moral and justified.
But the argument that a Union which was the consequence of voluntary assent can also be dissolved by removing that consent, would seem to me a very powerful argument.
Indeed, many Northern newspapers of the time agreed. Their Headlines were along the lines of "Go in Peace our Bretheren". Much of the North had no interest in forcing the South back into the Union, and were it not for the recalcitrance and hyperbole streaming out of Washington they would have left their secession a fait accompli.
A sh*t they really did not give till they were stirred up by manufactured outrage and ordered to fight.