You did not provide a prima facie constitutional case against secession, although I think there is a case to be made that secession was not morally justified.
Furthermore, the way you relegate the Declaration to obscure unimportance shows that you have little understanding of the dynamic moral connection between the Declaration and the Constitution. How can you make the connection between the Articles and the Constitution and not the Declaration and the Constitution? One cannot fully understand the Constitution without understanding the genesis and the importance of the moral principles behind it. Those principles are laid out in a basic form in the Declaration of Independence. It is not codified positive law, but it has the force of the beliefs and convictions of the men who wrote, debated and ratified the U.S. Constitution. The Constitution served to secure the God-given rights proclaimed in the Declaration. To deny its importance is to deny the importance of the moral principles which are the basis of the United States of America. Just because it is not codifed as Positive Law (it is a statement of principles and ideals not a demand for obedience to any laws). I think it is you who thinks the Articles and Constitution sprang ex nihilo since you place no importance on the Declaration of the principles behind these documents. Do you think these men were devoid of a philosophical worldview - do you think the Constitution is devoid of a set of ideals? The well established fact is that these documents are all undergirded by judeo-Christian philosophy, and I will not let you dismiss those noble principles as unimportant to the founding of our nation or to our present Republic!
First, no one who actually wrote the Constitution thought that secession was a legitimate option for a state. Madison's quote supplied by Ditto is rather telling.
Second, the South was awfully damn selective about secession. Some of Jeff Davis' statements from his time as Secretary of War made it clear that NORTHERN states that threatened to secede over the fugitive slave laws would be held in the Union at bayonet point if necessary. Fast-forward to 1860, and suddenly secession is a sacred right.
Third, states are admitted to the Union only by consent of the other states. What you're proposing is a massive disconnect in responsibility--that on the one hand, states can be admitted only with the consent of a majority of other states, but that they can walk out at any time on solely their say-so.
1860 was not the first time secession was contemplated. In the Hartford Convention of 1814, several New England states considered secession. The reaction by the rest of the Union was, to put it mildly, astonishingly negative. Nobody acted as if the aggrieved states had any right to secede.
Do you think these men were devoid of a philosophical worldview - do you think the Constitution is devoid of a set of ideals?
Actually, for its time, the Constitution was about as UN-philosophic document as you could get. Yes, there was a guiding philosophy behind it, as expressed in the Declaration--but the document itself is really rather good technical writing, explaining how a previously-unseen form of governance would work. That's the amazing part of the Constitution--not that it expresses a philosophy (it doesn't, except by inference), but that it was written well enough that it actually worked.
That still doesn't make the Declaration of Independence any sort of enforceable law, period.