uhhh....somehow i doubt you can change the koth zone randomly, you can't exactly strap it to an attach mover, because it's not a brush...hmm. Actually, i think i know of a way you can do it, have like five areas where you want it, put a koth zone in each one of them, then you've got to find a way to start with them all off, but to trigger one of them on when a certain thing is achieved e.g: a) after a certian amount of time that the zone hasn't been reached or b) after the 30 sceonds has been made inside the zone.
Maybe you could do this better (or at least help yourself out a bit) by coding some more into the koth zone. Try making a new zone (that expands zone) and make it do nothing, it's just a marker. Then, make the kothzone jump every a) or b) to a location of one of the blank zones. That way, they act like beacons, and if you're coding it, instead of just trying to do it with UED, you will have a lot more creative freedom and you can make it much better.
Hope that helps.