Hi David,
Lincoln was receiving death threats from the moment he was elected. Enroute to the White House there was a serious threat made against his life in Baltimore. He received death threats throughout his presidency and was finally murdered by a Confederate sympathizer. I don't think a speaking tour throughout the South would have resulted in "cooling tensions."
Lincoln's public speeches speak for themselves. Southerners were familiar with Lincoln because of the national coverage the Lincoln-Douglas debates attracted in 1858. In 1860 Lincoln's Cooper Union speech was printed in hundreds of newspapers across the country, including the South. The first inaugural was directed to the Southerners. Reread the final two paragraphs. His position was on the record and stood by it. What was left to say that he had not already said before?
I like your responses to the George Washington and Andrew Jackson alternate histories, thank you for having a good sense of humor! I like the part about Jackson, that's good stuff!
Best,
Sam.