The declaration was an argument. "For the following reasons, we believe we are entitled to be independent and, if you don't like it, come stop us. Strong letter to follow."
I cannot reconcile your statement above with what is written in that document. Once again we have a situation where both things cannot be true.
If the British Colonies secession from the British Union is not a case of expecting an "existing government" to "stop governing in a geographical area", I do not know what is.
That is exactly what we expected, and that is exactly what we got.
These people pledged their lives. What do you think they meant by that? They expected a fight.
Under the then British rules. But suppose Britain had a document called "The Freedom Declaration" which said that a Colony of Britain had a right to leave if the majority wished? Then Britain would have been in the wrong to stop them.
The British did not have such a document. *We did.*