From what I have read, the PCs are sent to a no man's land type of area, and they can conquer it and make it their own and set up their own kingdom there and deal with threats as needed.
This is essentially the thrust of the campaign for books 1 to 4. Books 5 and 6 deal with higher level threats to that kingdom and focus the adventure in a couple of specific directions.
So, I have some questions:
1) Has anybody done similar? (run Kingmaker for 4E)
I am currently GMing Kingmaker in its native Pathfinder rules supplementing the action with Open Design's Tales of the Old Margreve (a truly brilliant piece of work) as well as recently slotting in The Haunting of Harrowstone as a significant directed side-adventure. I have reduced the campaign XP track to "slow" so as to fit in the extra material as well as give the feeling of years (and even a generation or two) passing by as the full campaign arc develops.
2) How do you like Kingmaker overall (even if running PF or another system)
It is a lot of fun, most likely the best adventure path to be produced (the first module won an Ennie last year) and has all the makings of "classic" written all over it. Highly recommended! The thing is, half of my players are natural sandbox style players while the others are better when they have a solid path to follow. As such, I have mixed it up so that everyone is getting their gaming fix.
3) Is Kingmaker something I can easily merge into an existing game, even if it is 4E? I know I'll have to change the encounters around to make them suitable for 4E, but I'd have to tweak any standard module anyways, as I have a large gaming group.
Kingmaker is by it's very nature a simple idea that is easily merged (or perhaps more to the point, it is easy to drop ideas into it). There are two sets of rules that will exist outside of the running system: the Kingdom making rules (book 2)and the Mass Combat rules (book 4). Importantly, I think an adventurous 4e DM could fix some interesting skill challenges to these and really ramp the concept up to it's fullest. I think this aspect would be quite exciting. However, I think you will have a significant job with crafting encounters (more of this next point).
4) Would I be able to start with Kingmaker 1 and just up the encounter difficulty? Or, should I set some things up in game and start them off with (for example) Kingmaker 3?
I think you are going to have a handful of difficult choices here. Kingmaker 1 does presume an entry-level party. However, it would be quite easy to have this "no-man's land" be significantly more dangerous. In module 1, the central threat is a group of bandits that the party must deal with as well as the general exploration and mapping of the area. The sandbox nature means that upping the incidental and set hex-based encounters is very easy. However, what is a little trickier is working out where all of this is going to go. If the party have had a fairly quick path up to 6th (and soon to be 8th level), then stepping into Kingmaker is going to be noticeably slower. Time will go by exploring. Months of downtime as the Kingdom develops is going to be very strange if the players and their characters have the mentality of "let's go adventuring instead of waiting". If levels 1 to 8 have happened in a number of months (or possibly even weeks!), this is going to be a pretty jarring transition and is certainly something to be aware of otherwise. Obviously you can do this. In addition, you can hoist a whole heap of threads from their previous adventure into the "Stolen Lands" area (what you would need to do levels 7 and 8). Is this the "best" way to do Kingmaker? Maybe not but I'm sure it would still be good.
I think starting at Module 3 would be a poorer option and the campaign would lose a little of its exploration gloss. Carving out chunks of an AP really does leave a few holes in the overall story and achievement that the first two modules provide.
5) Any other suggestions? Am I crazy to consider doing this? The game is at the point where I'd like to get some sort of unifying campaign idea together.
You are not crazy for attempting this and I am sure you would have a heap of fun converting it over as well as putting your own stamp on it.
However, I have an alternative idea that may be OK (or not but heh...

).
Could you possibly start up a new second party of PCs for your player's starting at 1st level, playing through modules 1 and 2, with the aim of getting these additional PCs roughly in line with the first party? Then, each player has two PCs to run, two PCs that can take different roles with the kingdom. You can then have missions where the players choose one PC (and then the other for the next "mission") to go out on whatever the task happens to be. I think this might be an interesting way of having enough PCs to run their new kingdom as well as have others that can go out adventuring.
The other idea is just to bite the bullet and reset with new PCs from the start and try to more naturally follow the Kingmaker AP. That way, conversion will be easier, the various stories and threads within the campaign would still be applicable and you will have a lot more resources on the net (both Paizo's Kingmaker forum and various Kingmaker podcasts) that will feel relevant rather than not applicable or useful. While I think that Kingmaker would be relatively easy and fun to convert, complicating it by starting at higher level might just take a little of the fun and shine off.
What I thoroughly suggest though is listening to episodes 8 and 12 of the Pathfinder Chronicles podcast
here. They are a couple of hours each with the primary focus being Kingmaker modules 1 and 2 respectively. While it is Pathfinder-based, the advice is brilliant, the coverage deep and the fun bountiful. They talk with the module authors about each module and then talk amongst themselves what they like and dislike, what they would change and what really works. Easily the best gaming podcast I listen to (and I listen to quite a few).
The Kingmaker forum is excellent and I can see you have already found it (currently at
13,281 posts in
780 threads - that really is hugely significant).
[Alternatively, you could run it in it's native Pathfinder rules (our group plays both 4e and Pathfinder) and have an absolute hoot too]

Whichever way, I think it is definitely worth having a look at.
Best Regards
Herremann the Wise