Here's a webpage which makes your point, the electoral votes from New York, Ohio and Pennsylvania alone being more than the Southern states supporting Breckinridge combined, 85 to 72. Three key Southern states (Tennessee, Kentucky and Virginia) representing 39 electoral votes supported the Constitutional Union Party. Bell lost 9 electoral votes in Missouri by a margin of 429 votes of 165,563 cast in the state.
http://www.etymonline.com/cw/1860.htm

Your description of Lincoln's position as more pro-Union rather than anti-slavery is correct. Abraham Lincoln's positions on slavery were considered moderate within the Republican Party.

However, you misunderstand the dominant Southern political sentiment during the election of 1860, which was Unionist. Vice-President John C. Breckinridge campaigned as a national candidate, not a Southern secessionist. Anytime they were accused of favoring secession, States Rights Democrats vigorously denied the charge. To counter this, they accused abolitionists of wanting to vote the slave states out of the Union, a position espoused by some radicals.

The position being argued in Southern States was not secession, but slavery in the territories. Senator Douglas fared poorly throughout the South due to his position, which held that the people of a territory had the right to vote slavery up or down. States Rights Democrats derided this as "squatter sovereignty". The States Rights position held that residents of all states, slave and free, had a right to the territories. In other words, a slave owner could move to a territory and take slaves with him because slavery could not be abolished until statehood was achieved.

As for "National Unity", that was the position adopted by the Constitutional Union Party. The Bell-Everett tickett held the Constitution, law and order to be primary concerns. In the slaves states, the Bell-Everett ticket outpolled the National Democrats 515,747 to 163,404. It posed the most serious political challenge to the States Rights Democrats in the Southern states. "National Unity", as you describe it, did not become a dominant sentiment in Northern states until Major Anderson surrendered. After the U.S. flag was lowered at Fort Sumter most people who had been willing to let the Southern states go had a change of heart. It should be understood that at this time "National Unity" was as important in the South as it was in the North.