Whatever Lincoln did would not reassure the Confederacy that slavery was secure. The Corwin Amendment needed the support of 3/4rds of the state legislatures. It wouldn't get that. I suspect Lincoln knew that. He may not have thought it would get the required votes in Congress.
In any case, it wasn't a done deal: Lincoln couldn't just wave his hand and change the Constitution. And the idea of an unamendable amendment would have had serious problems in the courts. So in the eyes of the secessionists slavery wasn't secure if the slave states remained in the union.
You wrote: "Well this statement presupposes that the issue of slavery had something to do with the cause of the war." Slavery, the spread of slavery to the territories, and the permanence of slavery as an institution had everything to do with the deeper causes of the war -- why the country was so divided and why some people wanted their states to secede from the union, something which no president would allow a state to do unilaterally. So yes, slavery had something -- everything -- to do with the causes of the war.
Whatever Lincoln did would not reassure the Confederacy that slavery was secure. The Corwin Amendment needed the support of 3/4rds of the state legislatures. It wouldn't get that. I suspect Lincoln knew that. He may not have thought it would get the required votes in Congress. What was the vote in the Congress?
In any case, it wasn't a done deal: Lincoln couldn't just wave his hand and change the Constitution
Really? That's more or less what he did to pass the current 13th amendment. (Through the Senate anyway) Well, hand waving along with bribes, threats and coercion of Southern states by use of the Army, but yeah, he more or less singlehandedly amended the Constitution.
Slavery, the spread of slavery to the territories, and the permanence of slavery as an institution had everything to do with the deeper causes of the war
That makes no sense in light of Lincoln's efforts to protect slavery by amending the constitution. Even if you are correct that 3/4ths of the states wouldn't ratify it, it still speaks to Lincolns' intent.
You cannot rationally claim the war was about ending something the very man who launched the war was trying to further protect just a month earlier.
This is a dichotomy and cognitive dissonance that I find incomprehensible.