"that all those that were born under one natural obedience while the realms were united under one sovereign, should remain natural born subjects, and no aliens; for that naturalization due and vested by birthright,"
To my understanding, this could mean either of two things, neither of which is good for your argument.
1. "born under one natural obedience" means owing "obedience" by the character of your nature, (born to people who are already the property of the king) or
2. being claimed by the King as a subject through the process of "naturalization" at birth without regard to the will of yourself or your family.
The First explanation means that you have no other nation from which you may claim allegiance anyway. (Therefore you ARE naturally an English Subject.)
The Second explanation means you are claimed by the King through a process outside of natural law, and therefore contrary to the principles which we asserted to throw off the King's claim on US.
Remember, according to the common law, we were not permitted to throw off the King's authority. You are arguing that the King's law should be kept, though it serves none but the King's benefit.
A further analogy which I just thought up is like that of a cow that births a calf on your neighbors property, all to be claimed by your neighbor. The cow may be free to go back to it's rightful owner, but the calf is now being claimed by the neighbor as his own. (To a kingdom, cows and people occupy the same theoretical footing. :) )
Is this natural law when applied to cows? If it doesn't make sense when applied to cows, I don't know why you think it makes sense when applied to people. :)
And this is why your arguments are flawed.
You are using a strawman argument (claiming I say the King's law should be kept) and trying to say from that that the US does not use common law. Since it obviously does in many things, this argument goes nowhere.
You may not like the "born in the ligeance" phrasing when it applies to a king, but the US has used the same phrasing. WKA quoted an early American legal scholar, James Kent
Natives are all persons born within the jurisdiction and allegiance of the United States. This is the rule of the common law, without any regard or reference to the political condition or allegiance of their parentsand
all persons born in the allegiance of the king are natural- born subjects, and all persons born in the allegiance of the United States are natural-born citizens.for example.