George, I cannot prove slavery caused the war because it did not. The only thing that caused the war, technically, legally and morally was Secession. And as you point out, as evidenced by the documents presented by you so clearly document. So everything else.
It can be argued that the South was the cause of the War due to their Secession.
It can be argued by South that it was the North's fault for pushing them to fight, and then you have the endless loop,, who was right. Arguing who was at fault cannot change a thing. Each side then, and now thing they were correct and justified in their actions. We cannot change what happened then. We are at the point we need to fix the problem to keep it from happening again.

As I stated before people mistakenly believe that since each Confederate States mentions of Slavery, that slavery was the cause. I am going to present what Arkansas had as a resolution on March 09 1862 introduced by George B Smoote:
"Resolved that the Platform on the Party known as the Black Republican Party contains unconstitutional dogmas, dangerous in their tendency and highly Derogatory enunciation of the right of the African Race of their country to social and political equality with the whites."

State of Alabama Ordinance:
"It is the Desire and purpose of the people of Alabama to meet the SLAVE HOLDING States of the South, WHO MAY APPROVE SUCH PURPOSE, in order to frame a provisional as well as Permanent government UPON the Constitution of the United States."

I think you can agree that Slavery was artificially thrown in the political mix, and was not as important as it appears to have been. It was the focus, of the North, and the South in their self defense, had to counter it. There was a lot more politically and economically and socially going on. In many of the book of a history of the war, that I have read ( ex. McPherson, Nevins, Catton, Ward, Freeman, Edwards, etc) contains discussion of slavery and the polarizations of North and South by views on Slavery.
However, with that said, It can be highly argued that slavery had everything to do with Secession. Because Slavery was a major factor in Secession, and Secession caused the War, then slavery was a major factor in the War. that is why I said: "The cause of the War had Nothing to do with Slavery/It had everything to do with Slavery.