I'd dispute the claim that Civil War was fought over issues of slavery. Whilst the persistence and creep of Slave power certainly played a role in the rising tensions between the Free and Slave States, most notably in the nullification crisis over the Fugitive Slave Acts and the Slave Transit Act, it is worth remembering that radical abolitionists were among the staunchest supporters of the Union as they saw keeping the Free States in the union as the best bet for abolishing slavery. There's also the fact that a whole bunch of Free States were opposed to secession, such as Iowa, North California, Oregon and Deseret.
The Civil War owes its origins to the increasing centralisation of Federal power in the hands of the Presidency and who tended to be overwhelmingly in favour of southern interests at the expense of the north. To prevent that you would need to prevent the Jackson and/or Calhoun administrations, both of which heavily entrenched the nationalist consensus and ruthlessly pursued pro-southern economic policies to the detriment of the north. Alternatively an earlier Clay administration might have been able to patch things up as a lot of his compromises might have worked a decade earlier instead of being too-little-to-late. There's also the issue of certain New England politicians, I'm looking at you Hamlin, who mobilised nascent New England nationalism and resentment to the south as part of their campaigns, which ultimately fed into separatist sentiment.
I'd also dispute the idea that it was superior manpower and manufacturing that won the Free States their independence. True they had a slight advantage over the union in terms of raw numbers but it is worth noting that there were still plenty of unionists in the north who fought for the union, New York basically had its own personal civil war going which is the reason why the city is a US enclave deep in Yankee territory. Furthermore, northern manufacturing, which had been stagnating for decades under Federal misrule, only really took off after independence when the FRA was able to pass the protectionist agenda that the north had been trying to get for decades. The thing that really kept the North in the war for so long was British support, with Britain's entry into the war ultimately leading to the armistice.
OOC: I kind of figured that any plausible scenario that has the north secede from the union would require that the northern states were much weaker than ITOL. What I'm imagining is that Jackson wins in 1824 instead of Adams and is reelected in 1828. Calhoun takes over after, rallying the anti-Jacksonian forces to his side, but unlike OTL he largely remains a staunch nationalists instead of a States Rights fanatic due to the Federal Government agreeing with his policies on slavery and tariffs. The Panic of 1837, which disproportionately hit the south, is reduced due to Jackson's refusal to recharter the Bank of the United States gets overturned due to having made too many enemies by the time it comes up as well as the Federal government taking a proto-Keynsian interventionist response, which results in heavy infrastructure investment, primarily in the south, paid for his higher taxes that disproportionately hit (or at least are seen as hitting) the north. In addition Illinois ends up reverting back to a Slave State after its admittance, which destroys the idea of trying to balance Free and Slave States especially after slavery is legalised in the territories (for the purposes of encouraging economic growth and settlement as some people believed it would). The sum total of this is that the north is economically weaker and attracts far fewer immigrants than IOTL, whilst the south is in a much stronger position within the Union. Eventually northern discontent is able to make an impact when Henry Clay is elected President, promising to rebalance the power between the states and address northern concerns, but his measures are widely seen as ineffective and ultimately does more to undermine northern faith in the federal government.