I quite like the notion of Karrnath as a kind of regimented, militaristic nation giving off vaguely vibes of Tsarist Russia, or perhaps Prussia on the eve of the unification of Germany. There's a kind of dark, tragic pathos to the country that rings as fascinating, although I admit that I'm not always 100% sure what to do with it. I dislike immediately casting the Karrns as villains, because that doesn't really describe them, but as honorable yet dark antagonists or rivals, perhaps they work a little better. King Kaius the I(III) is a tragic hero, in fact, although of course he's also a monster.
I'm actually remixing very little of Karrnath, because it works quite well even in my system as it's printed. A few minor things, though—both men and women don't have mandatory military service, because unlike today's delusional neurotic people, the Karrns, as all actual soldiers would immediately know, keep women out of the military except perhaps in medical care roles, like the old WAC. Indeed, given the large numbers of Karrns who were killed the war and resultant famines, women are strongly encouraged by many social cues, to marry young and have large families, raising the newest generation of Karrns to replenish the numbers so that the reliance on undead troop fodder is not nearly so necessary (although Karrnath is unlikely to abandon that either, because it has worked quite well for them, and is popularly seen by the citizens as not only evidence of their ruler's pragmatism, but also his dedication to preserving the lives of his citizens.)
The Twelve is, again, not exactly a wizard school or organization because we don't really have wizards, although as a source of magewrights it is famous for turning out much more "mechanics" than anything else; i.e., people who use magical items. Many of the mechanics from Karrnath are more likely to make their own magical items, and are therefore less adventuring than most, being rather middle-class craftsmen as their primary source of income. Many of the eccentric mechanics, to the extent that you can even call this group "many", utilize items made by magewrights trained by the Twelve and still operating out of Karrnath, and it is an interesting although significant source of exotic exports by the country.
Finally; religion. The book suggests that the Church of the Silver Flame is relatively rare in Karrnath because of their rivalry with Thrane. This doesn't make sense in my Remixed setting, where rather than have the Church of the Silver Flame be a kinda sorta obvious Christian stand-in, it's actually just Christianity, but rather than being a European, centralized, Catholic style Christianity, it's an American, decentralized Protestantism with local pastors. Certainly religious people of Thrane and Karrn may find themselves at odds for political reasons, in spite of their shared religion, but the majority of people in Karrn are Christian, and Karrn is a Christian country. The Blood of Vol is seen less as a religion and more of a social club like an amped up version of a Masonic-like society; kind of like the Shriners or something. This is mostly a major change and remixing of Thrane than of Karrnath, but this is the specific implication of it as applied to Karrnath.
Karrnath population remixed (not counting undead)
87% Human
7% Jann
6% Other