This is rough, but it looks like the area only takes up about four 30-mile hexes on the Darlene map, so yeah, honestly you could probably fit it in the Principality of Ulek if you squinted and changed some names. It wouldn't be in the Kingdom of Soes, for example, and the Merciless Range would be the Lortmils.
If you're going to do that, though, it might be better to change all the names and pretend the stories took place in a canon city like Gradsul or Gryrax. Or Greyhawk, for that matter.
The Oeridians are supposed to be from further west in Oerik, and some of the Suel could have fled west instead of east. The Celestial Imperium is implied to be Chinese in flavor, but as an empire it could encompass a number of different cultures. It's conceivable, then, that the Kingdom of Soes could be part of or adjacent to the Celestial Imperium on the western side of the Sea of Dust. The biggest problem is the Flan deities worshiped in New Koratia; there shouldn't be any Flan in that region, so although those gods might be worshiped there, it probably wouldn't be under those names (it'd likely be Sol instead of Pelor, for example). In general, I'd expect the resulting culture to be somewhat of a funhouse version of Flanaess culture, with some Chinese influence from their Celestial/Suhfangese overlords.
In this thread
I suggested a few other possibilities. The Tharquish Empire might fit, if you ignore that it's supposed to be Roman/Latin in culture in the Black Moon Chronicles.
ripvanwormer wrote:The islands might be a possibility. The WotC page that I linked to above mentioned "rich lands across the Southern Sea" and "war galleys from the South," and you can't get too much further south than that. It might refer to a more southern island, however. If the Southern Sea is the Gulf of Ishtar, the war galleys might have come from the region north of the Barbarian Seameast, which might be wealthier than we generally assume.
Tharquish is supposed to be similar to the Roman Empire in culture, though, and it probably doesn't have the same mix of deities that the Flanaess has. The Black Moon Chronicles that inspired this part of Oerth posited a monotheistic faith called the Order of Light, as well as a more pagan Black Moon cult, an imprisoned demigoddess called the Oracle, the worshipers of Lucifer, the neutral-aligned Dragon-Knights, Pharoah-worshipers, and the order of the mage-deity Methatron.
The other possibility I suggested was a breakaway kingdom on the island of Thalos. Perhaps the Kingdom of Soes is part of the same island but with an independent monarch.
I'm going to defer to Big Mac, who has read the books (since I haven't), but I think it might be reasonable to assume the books' mention of Ratik being east of the Kingdom of Soes might just be a mistake from an author who plainly knew little about the geography of Oerth. On the other hand, Oerth is round, so technically things that are to the west are also to the east if you go far enough. If the main characters traveled east the long way around the world, they'd eventually reach Ratik even if it would have been more efficient to go west.