European morals on the subject are well in evidence, during the actual war, even after Lincoln frees southern slaves - European merchants were more than willing to purchase confederate cotton that was shipped overland to Mexico to be exhanged for arms.South can't survive. Slavery is generally reviled in Europe. The South needs to sell its cotton to Europe in order to survive. The British can get cotton from Egypt and South-East Asia(?). By the time of the American Civil War, the South was no longer the King of Cotton. The Brits and other Europeans can start getting their cotton from somewhere else if they don't want to trade with dirty slave holders. The complete collapse of the Confederacy follows.
Popular sentiment may well have been against trading with dirty slaveholders, however history is littered with profiteers willing to make a buck.
Following the Trent incident there was a limited call for intervention. Palmerston actually sent token troops to Canada in order to give a bit more substance to diplomatic pressure being applied to Washington.It was already politically ridiculous for the Empire to interfere; whatever Americans were discussing as the reasons for the war, there was a strong sentiment in England that it was about nothing more than propping up slavery.
In any event prior to Antietam the Palmerston cabinet was actively discussing intervention, offering to mediate with the implicit threat of recognizing the CSA. No less a personage than Gladstone publicly came forward towards recognition and all the intervention that entails.
It enjoyed a brief heyday and when it reached the cabinet it was tabled with a "wait and see" approach. In the interim Lee's offensive faltered, Lincoln played the abolition card, and poor European grain harvests resulted in massive grain imports from the North. In Palmerston's own words:England basically went in and profiteered from the war, knowing the Confeds would sell cheap to anyone with cash. The movement to support the South never gained political acceptance.
"It is evident that a great conflict is now taking place to the northwest of Washington and its issue must have a great effect on the state of affairs. If the Federalists sustain a great defeat, they may be at once ready for mediation, and the iron should be struck while it is hot. If on the other hand, they should have the best of it, we may wait a while and see."
British intervention via recognition and direct armament supply was still a possibility until Antietam.
Frankly I'm not sure the Deep South would break up and die. I see very little that makes them worse than several of the contemporary Latin American nations. Sure they'd suffer from terrible economics when the agricultural market goes south, and there would likely be plenty of incidents over borders in the territories, abolitionist activity, navigation on the Missippi; but that is all survivable. It is not like they would be the only nation in the world to have a lousy hand and stay in the game.