Another possibility to accomplish the same goals would be to have Douglas somehow win the nomination and strike a last minute deal with the Southern delegation to keep them from walking out. If Douglas manages to win the presidency in 1860 (somehow...), then it's really just a matter of time before the whole thing blows up in his face.
Douglas will stake his entire presidency on the idea of popular sovereignty, which would have been workable a decade before. Now, however, the stakes are too high for both free states and slave states; neither can afford to let the other side "win" a state. So you get violence just like you suggested. Then, as tensions mount, Douglas dies leaving his Southern VP (changed by the different convention ITTL) in charge of the country. As the situation reaches a boiling point, the pro-slavery president comes down hard on the side of the slave states, angering the free states and making secession look more like a reasonable answer. As the tensions continue to mount, riots begin to spring up around the north. The army is sent into northern cities to pacify the "rebels," only spurring on the talk of secession.
After the election 1864, the Democrats win again by virtue of an election thrown to the House of Representatives and the northern free states, at this point completely disenfranchised, follow through on their threats beginning with New England and working down into the midwest. The new government is likely situated in Philadelphia, New York City, or Boston. The federation is led by Salmon Chase, in fact a moderate but the most able man the new nation has as an option.
And I'll stop there. That's just my path of getting to the same place as you, only I think that a Douglas administration makes a more coherent story. It's a promise of successful reform only to have it yanked out from underneath your feet at the last second. Is there any doubt that Breckinridge's administration would result in catastrophe? No. But Douglas seems like a set up for success, and I believe that the disappointment experienced from the failure of that success would be a more effective trigger for the northern secession than the anger over Breckinridge.