I just ordered all six Kingmaker modules and am awaiting their arrival in the mail. So I haven't yet read any of them, but I'm planning on running it soon and so I've been spending hours and hours and hours going through forums and discussions and reading everything I can find on making it run well. So while I certainly could be entirely wrong, I do feel like I've already got a very firm grip on what may work or not work with the AP.
From everything I've read, it seems that the XP track in KM strongly assumes that the characters find and do EVERYTHING. As long as they do that, levels work out nicely. But what are the odds of that happening? Unless I railroad them heavily (which runs entirely contrary to the whole point of sandboxing), they are likely to miss stuff. By the time they reach level 5, the AP may expect them to be level 6 or even 7.
The rest of this is spoilery of both KM and CoT (which is kinda weird since I haven't actually read either of them yet), so I'd better tag it and say the rest of this is strictly DM-only:
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The other biggest complaint I see about the Kingmaker AP is lack of foreshadowing of book 6. The need to add additional foreshadowing of that book is the main reason I ordered all six books before beginning the campaign - I want to know exactly what goes on when, so that I can add lots of foreshadowing.
That being the case, throwing Carnival of Tears in as a Kingdom Event when the players reach level 5 could serve two important purposes: It can catch the characters up to where they belong XP-wise, and it can also serve as additional foreshadowing of book 6. It's hard for players to say that they were blind-sided by a world of angry fey trying to take over a kingdom when they've already suffered character deaths due to the existence of angry fey trying to take over a carnival.
It seems like an incredibly natural fit.
That said, if my players' characters DO manage to keep up on XP and don't need the additional levels to catch up, then I wouldn't feel a need to run Carnival of Tears since foreshadowing can be done in plenty of other ways. So I'm going to wait until they are 4th level and see where they are in KM before I decide whether or not I need to buy CoT.
Of course, the mental makeup of your players is another aspect of the decision: All four* of my players are SERIOUSLY into sidh and fey mythology, and all love exploring the dark side of the fey. I seriously doubt there's ANYTHING in CoT that could actually offend any of them. Not that they aren't impossible to offend - they are nice people after all - but they are also very jaded. I just seriously doubt that Paizo would even consider publishing anything offensive enough to overcome my players' jadedness. If the fey are anally raping children with graphic descriptions or something that shocking, and it's somehow too central to the story to gloss over, then I'd definitely skip CoT. But that's not something I can imagine a company like Paizo doing. (I would totally expect that kind of thing from a company like Lamentations of the Flame Princess, just not Paizo.) And if it's just gore (even gore involving genitalia or something equally tasteless) then it might make my players go a little pale, but then they'll get over it and have fun future stories about that time the game got really unexpectedly dark. If your players are young, or not that jaded, then this should definitely be a consideration.
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Just my 2¢.
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* (Actually, three players at this point, but I'm hoping to recruit a 4th - and possibly 5th - and the two people I have in mind for that are also into exactly the same things.)