This is where I lit on the idea of the "altquel". That is, a sequel that follows the same events from the first film (perhaps from a slightly different perspective) up to a critical moment in the film, where a key even causes the two films to diverge. Essentially, it's the story of an alternate timeline or universe in which the same events lead up to very different results.
So why an altquel for Cabin in the Woods, specifically? Without indulging in spoilers, all I can say is that there is a moment in the film where we get a glimpse of what might have happened, had any one of several other actions been taken. It's a perfect jumping-off point for an altquel!
But, Cabin in the Woods is really more than just a horror movie. It's a postmodern, revisionist take on the state of the horror movie genre, so why go with a straight altquel? Why not tell all of the stories at once? How? OK, that will require spoilers, so let me give you some time to go watch the movie, first...
Now, on to the spoilers!
At the end of the film, the human race is doomed by the return of the "old gods". But how is the human race doomed? Do the old gods represent a simple invasion by a superior physical force or will they so fundamentally change the environment of the world that humans cannot survive? Science fiction has often dealt with the idea of beings who show up on Earth and disrupt the atmosphere or sun or some other environmental factor, but these are gods... what fundamental changes might they bring?
Here's the capsule idea: the old gods emerge from their slumber, immediately changing the laws of physics in the region of Earth, much the same way we might change a thermostat. This has an impact in four dimensions, including that of time... our heroes are not only killed in the present moment, but their previous lives are rendered uncertain ("unstuck" to use a genre cliché), and we see all of the possible ways the first movie could have played out (metaphors related to ripples on a pond ensue...)
We observe every one of the artifacts in the basement being selected in its own, seemingly isolated timeline. In each timeline, something different goes wrong, and a different outcome results, seemingly inevitably, in the release of the old gods from their slumber (maybe as a vehicle for each character to have their own final scene in the facility). But in the final version, Marty selects some innocuous looking trinket, triggering a version of events in which he brings about some sort of paradox, eliminating himself from the multiple realities formed by these alternatives. Once isolated from events, he finds a way (perhaps in The Director's office there's a special sort of monitor?) to observe all of the timelines and their consequences.
From there, you can go any number of ways. He might choose to prevent each of these realities from occurring. However, I'd find it more in-line with the kinds of horror tropes that Whedon and Co. are clearly trying to poke at if he managed to solve the problem which causes the end of humanity, only to find that he must remain and act as the new Director, replacing Weaver's character for subsequent annual rituals until someone once again "beats the system".
That's what I think would make a decent altquel to Cabin in the Woods, but then you could probably come up with a dozen of your own ideas...