The problem with the idea is that you're overvaluing individual events (the Missouri Compromise) as causes of the Civil War and undervaluing general trends. The sequence of events in the 1850s - California, Kansas/Nebraska, the Fugitive Slave Act, Dred Scott - would not have gone away if the Missouri Compromise had gone in a different direction. For one, they happened 30+ years later, so the causation has to be more complex. What happened was that the North was growing faster than the South in population, swamping it in the House. Zachary Taylor was the last Southern president until LBJ; the presidents in the 1850s were doughfaces rather than Southerners. Within the North, the fastest-growing region was the Midwest, which had more to fear from the expansion of slavery than New England, for two reasons. First, it had claims to expand to the Great Plains and so did the South (Missouri would've been a point of great contention by the 1830s, but in 1820 there weren't enough people in Illinois who'd care). And second, it was politically younger and not enamored with the century-long compromises the New England and Mid-Atlantic elites had made with the South. Of note, the most intensely anti-slavery parts of the Northern US were not the coastal cities, but the interior: Upstate New York, and the Midwest. At the same time, the Southern economy required the expansion of slavery into new territories, hence the Southerners' attempts to swamp the Great Plains and the Southwest and calls for annexing Cuba.
So let's say the Missouri Compromise goes your way: Missouri gets delayed until Michigan can come in, resulting in a new pairing of free and slave states. By the 1830s, there already are enough Midwesterners that they'd at least try to swing Missouri their way. OTL Missouri never had much slavery, unlike the 50% black Deep South. Presumably the Southerners would win, but the Northerners would remain embittered. Then the new pairing of free and slave states creates some really low-population states, ones that by previous precedent should have remained territories for decades. Finally, the US conquers territory to the south (Cuba) but not the north (British Columbia); 54 40 or Fight was a Northern slogan, complaining that Polk was refusing to fight for territories that would be US free states, only for ones that would be slave states. Presumably, laws on fugitive slaves happen as in OTL, and are most likely harsher given that you're empowering the South more; the North would not be happy, and would be pushing for swamping borderline states. By the 1860s, it would have a solid majority in the House, and a leadership that would flatly not let New Mexico and such in. The constitutional crisis would have happened around the same time as in OTL, give or take 10 years. Might have been a war, might have been something else, but the antebellum political structure would not survive intact.