Other countries managed to get rid of slavery in less violent ways.
Slavery in the US is a pretty weird thing. There were a
ton of times that the US almost stopped slavery on it's own, but then something would happen to bring it right back. Like, you'd have people start pushing for relaxing some of the restrictions on slaves, only for a horribly timed slave rebellion to spawn and erase all thoughts of that. Or the economic benefits would seem to be too small to justify slavery, only for some new invention to boost demand for cheap agriculture.
It's kind of sad, and the UPM could certainly avoid that fate if they can avoid the same problems that cropped up in the US.
However, recent events will almost certainly make that harder.
The UPM just bought slaveholding colonies from the Hex, likely with some sort of assurances about keeping cultural traditions or something. This is a pretty strong cultural divide that is only going to be made worse as the non-slave northern colonies grow. It will only be made worse with expansion, as the issue of slavery for the north was always about restriction, while for the south it was about survival of their institutions.
And if the cotton gin gets invented soon, which is fairly likely, then we are going to see an increased demand for southern cotton.
The only good thing I can see is that the Khem got in on the cotton growing early. This should reduce demand for UPM's cotton, and even if it still increases slavery, the south UPM might think twice about rebellion.
A large part of the southern strategy was to use its role as THE cotton producer for Europe to force Britain and some other European powers to recognize them, and either intervene or at least pressure the Union to lift its blockade. The assumption was that southern cotton was too vital to the European powers, so they couldn't allow for production to be halted.
This, of course, was completely wrong, as the Europeans, while annoyed at the disruption, did not intervene, and instead started Indian and Egyptian cotton production to replace it (a disaster for the post-war south, as it was unable to make any money to recover in the aftermath of the war due to the now flooded market, and thus had great difficulty in rebuilding).
It also made the mistake of assuming that the Europeans wouldn't care about the slavery issue, which was also wrong, and is considered one of, if not
the main reason for Britain not intervening, as while many of the leaders were, in fact, pro Confederacy, the lower classes would have nearly revolted had they supported a slave state. And without British intervention, the French wouldn't do so, nor any other nation.
Tl;dr It's likely that, given current trends, the UPM will have a civil war.