Some good advise above, to which I will add only one thing, and its viability depends on how often you have a full 6+ group.
You can keep the players one level lower than the books recommend. This may come about naturally, depending on how swiftly they approach certain goals. The only real issue is when you have four players show up for a game instead of all eight. They might find it tough then, even if you use the encounters straight from the book.
Humorous Suggestion: Every baddie in the book has a twin! Hey, The AP is closely tied to the realm of the fae; it's not THAT out of whack!
"Hi, I'm Joe, this is my twin brother Ted. We'll be your bandit attackers for the evening." :)
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The best advice would be to look in the Advice section of the message boards for running large groups. The suggestions there work just as well in Kingmaker.
One specific piece of advice for Kingmaker (my group is 9-10 depending), is that you cannot just "add a few more" and expect it to challenge your group. You will basically have to rewrite some of the set encounters if you want them memorable. With a very large party, several extra smaller groups of mooks that can wade into combat a round later at an inconvenient spot, flying allies, or a spellcaster or two added to an otherwise pure melee encounter can spice them up.
For wandering monsters, you don't really need to mess with much. There are a fair number of hard as hell encounters there that can still tpk a 10 man party, like trolls and shambling mounds. Even if they manage to take them down, a couple are going to die.
One interesting note is that most large parties have at least a teensy bit of conflict in it. Have fey play practical jokes on the party that frame other players who might have some friction with each other. It shouldn't result in a open conflict, but can definitely make memorable non-combat encounters.
I actually found Kingmaker to be one of the better APs for large groups, thanks to it's Sandbox nature. I ran not one but two large groups competitively (and with flunkies) through parts 1 & 2 without too much trouble. Things I found I needed to consider though:
1) Wandering Monsters are your friend. They do very well for helping make up for lost xp due to excessive party split.
2) Side-adventures: due to excessive xp spread from having such a large number of PCs wandering around, tucking in a few extra encounters, side-treks & modules actually works out nicely.
3) use Table 12-2 for Abstract xp, rather than divvying xp up exactly. I've found many players get cranky if they feel other players are "stealing they xp" due to party size. Especially in the 6+ groups, it's just easier (math wise & socially), and keeps the griping down. Also keeps the group leveling within a reasonable pace for the AP.
In general remember less xp per PC will mean a Medium advancement track can feel like your on slow, so you might consider kicking the advancement track up by one (med. to fast) - only problem with that of course is if your group ever drops bellow 6, suddenly their zipping more quickly through the campaign, level wise.
Wealth is a different matter, as far as Kingmaker is concerned. Once they get that city you and they can use that as a lever to re-balance PC wealth for what ever shortcomings a large party might otherwise generate.
I run a game with 9 players, on a rotating schedule. Not everyone shows up all the time, but I usually have 4-7 players. I stopped giving out experience and treasure in Kingmaker. Our magic economy works as such: if you have the buildings that can produce it, you can get items, limited in nature, appropriate as you progress. At the beginning of the second AP I let the PCs get decked out in magic equipment, and it is only near the end they are starting to loose some of their effectiveness. They also cannot sell magic items through the kingdom. It keeps them from building too fast, reduces the disparity for those that cannot come often, as well as eliminates the need to track GP. I also use monster treasures to give out the sorely needed equipment, as well as the flavorful fun items.
But the harder thing to track is exp. Since I never know who is showing up till about 48 hours before hand, my encounters are always changing on the fly. This I can deal with. I always factor in monsters that I can increase the quantity of to make the fights balanced how I like. It did, in the first AP, get really hard to know when players should level up, so since the Stag Lord I just eye-ball what level they should be and at the end of a session tell them if they level up. It also makes it easier, since a great many of our encounters are role-playing, and those are notoriously hard to give exp. for.
All said and done, the biggest thing a GM has to do for this game is raise the ECL of ALL fights. Otherwise any 'random' fight on a hex is too easy. The PCs usually end up having a 15 round work day, and that will barely deplete their resources in the long run. It ends up being explore-fight-roleplay-camp every day. Not a challenge. Placing 'imposed' time restraints is a good way to keep your party from doing this.
For a party of 4-5 PCs, I use a CR one level higher as a daily fight. 6-7 I go two higher. For 8-9, I go at least three, sometimes four. And this is just for 'daily' fights. If there is a series of short fights (like various cave encounters), you usually don't need to go this high.
And the last piece of advice: quantity over quality. A high CR monster can challenge the whole party, but they have a severe advantage because of the number of actions the party gets as a whole. a CR 6 with one monster vs. a CR 6 with 6 monsters are two very different challenges.
Example (with spoilers): There is a fight in RRR where the paprty has to fight a Will-O-Whisp. They are level 5, and there are 5 of them. Instead of as-written, I had 2 W-o-W (CR 6 each) that would leave at half hp, and 2 Lurkers-in-Light from Beast. 2 (CR 5 each). The two complemented perfectly. I'd figure this was a ECL 8 for my party, a difficult fight, exactly what I wanted. By the end, one W-o-W left at a handful of HP, the other 3 were dead, and 1 party member was at 0 STR exactly (L-o-L have a nice poison). This was precisely what I wanted, and was an encounter I built on the fly, so I guess I got lucky.