You seek to apply the Constitution of the United States to a state that has seceded. In other words, you are applying a law to someone or something that is not in your jurisdiction. That's like saying the laws of California apply to someone living in Georgia.
But let's look at what the Constitution really says about whether the states have a right to secede, shall we?
The 10th Amendment says, "The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people."
Does the Constitution prohibit the states for seceding? No. As you point out, there are things they may not do while they are states, but there is nothing in the Constitution that says they may not secede.
Therefore, the Constitution clearly implies that states may secede.
Furthermore, as Professor Williams points out in his article, the question was discussed during the ratification process. People were repeatedly assured that the state retained the right to secede from the Union. This was the general understanding until Fort Sumter.
The problem is that you don't seem to understand the Constitution or our Constitutional form of government. The states are not creatures of the federal government. The federal government did not create the states. It was the other way around. The states are sovereign entities. The federal government is a creation of the states and of the people who live in them.
The states and the people who live in them may decide that they no longer want to be part of the United States.
Does it? The 10th Amendment speaks of powers not reserved to the United States. But it is clear that the Constitution reserves the power to make or unmake a state to the Congress. States cannot become states without a vote of Congress, they cannot join together, split apart, change their borders by a single inch without consent of Congress. Congress clearly implies that the power to unmake a state must lie with Congress as well. So for the southern acts of secession to be legal they would have required the consent of Congress.
Why? The United States already existed when they adopted the Constitution. That being the case, why not start with the establishment of the United States?
That's like saying the laws of California apply to someone living in Georgia.
You mean the laws of one state aren't applicable in another? Does that mean that forty years ago when people went to Reno for a "quickie" divorce to get around the waiting periods of their home state that the divorce wasn't recognized when they moved back? If so, a lot of people are in trouble. (All right, so that's a nit in the overall picture. But you'd have done better to use Brazil and Georgia as examples.)
Does the Constitution prohibit the states for seceding?
In accordance with the underlying principles of the Declaration of Independence, probably not. But does that mean the other States have no right to insist a State attempting secession be held to the agreement to unite in a perpetual union? Again, probably not. (A lot would depend on the circumstances.) It boils down to a conflict of rights and obligations. In the absence of applicable law, (and there is a lot of conflict here about the applicability of the law) it further boils down to resolution by peaceable means or by what some used to call "judicial combat."
Therefore, the Constitution clearly implies that states may secede.
If that were true this thread wouldn't be over 500 posts long.
The states are sovereign entities. which voluntarily entered into a Perpetual Union with each other, which union was established prior to and irregardless of the Constitution.
The states and the people who live in them may decide that they no longer want to be part of the United States.
You or your spouse can decide that you no longer want to be part of the "till death do us part" perpetual union you established, but that decision alone does not mean much.