
Box o' Flumphs |

Neither of these are so much during the APs themselves as potential continuations after their respective sixth installment, but:
Spoilers for a recent and a not-so-recent AP:
Both Curse of the Crimson Throne and Jade Regent conclude in ways that have the PCs very close to the new rulers of Korvosa/Minkai, or possibly even being those rulers themselves. The kingdom building rules could be used to represent the rebuilding and expansion of the new Korvosan order, or the reassertion of imperial authority in Minkai. Of course, the obvious downside to either of these is that it changes the kingdom building rules from a fixture of the main campaign into more of an endgame reward, so some of the player investment in building up their newly-acquired holdings might be diminished.

lordzack |

For using the kingdom building rules in established kingdoms, you might want to tweak the population per hex a bit. A low population density makes sense in kingmaker, when you're taking control of an unpopulated area, especially given that medieval population growth tends to be extremely slow. However, if you're ruling an area with an established population, the number of people per hex could range from somewhere like, 4000 to 15000. Whether this actually effects anything with regards to the rules, that depends on the DM.