The Colonies were already at war with Britain for over a year when the Declaration of Independence was signed. If the signers had survived into the 1860s they would have urged Southerners to be prudent and not rashly plunge into conflict.
The Founders didn’t forget that the didn’t write secession into the Constitution. Madison was quite clear that the Constitution didn’t allow unilateral secession at will.
The Hartford Convention rejected calls for secession. I also hope that if New York ever felt dissatisfied with the union that they’d try to work things out in Congress, rather than declaring themselves independent and seizing or bombarding the Statue of Liberty.
Also, was the government really that corrupt or tyrannical in 1861? And if it was, wouldn’t the slaveowners who had controlled the government for so long bear a big share of the responsibility?
No doubt they would have done, but the Southerners appear to have been wanting independence for many decades prior to the Civil War, so you could hardly call them "rash". If anything, they waited too long. They let the other side become insurmountably powerful instead of striking out when the forces against them were too weak to stop them.
The Founders didn’t forget that the didn’t write secession into the Constitution. Madison was quite clear that the Constitution didn’t allow unilateral secession at will.
While Madison's contribution to the effort was very significant, Madison was not the authority which granted the Constitution it's powers, and what he believed is irrelevant when compared to what the people ratifying the document believed.
With three states making it quite clear they believed secession was legal, (and for that matter, see Madison's quotes up above) and the other states not objecting, it is quite reasonable to believe that secession was legal under the Constitution and that nothing in it contradicted the Declaration of Independence.
In fact, you have to reach a lot to suggest there is any evidence that secession was illegal. The bulk of the evidence is on the side of legal.
The Hartford Convention rejected calls for secession.
Meaning they recognized it as a right which they chose not to exercise.
Also, was the government really that corrupt or tyrannical in 1861?
I've found indications it was corrupt far earlier, but not on the same scale it achieved in the 1860s. The 1860s appears to have been the pinnacle of crony capitalist, kickbacks, influence selling, theft, bribery and other sorts of corruption. Lincoln was highly amused at another cabinet member's characterization of Simon Cameron, "he wouldn't steal a red hot stove." And yes, Simon Cameron was very corrupt, but Lincoln's reaction tends to make you think he didn't see it as that big of a deal.
And if it was, wouldn’t the slaveowners who had controlled the government for so long bear a big share of the responsibility?
The same sort of responsibility that slaves would have for their work in making their masters wealthy.