I LOVE campaigns... we are currently running a large-scale 3 sector campaign using the Forgeworld (horus heresy book 4) "Conquest" campaign system, which is really just amazing. You don't need to play 30K or the 30K-narratives to use it; in fact every game
could be Kill Team style if you wanted and it'd work just fine, or some sort of escalation etc...
I wrote quite a bit about it in my blog haha... in fact with just that information and some of your own ingenuity (creating warzones) you could easily run that system without the HH4 book. This might help:
http://atticwars40k.blogspot.com/2016/05/conquest-campaign-for-dummies-part-3.html
http://atticwars40k.blogspot.com/2016/04/conquest-campaign-for-dummies-part-2.html
http://atticwars40k.blogspot.com/2016/04/conquest-campaign-for-dummies-part-1.html
If you're looking for cool narrative ideas, I think this one is just perfect for a Kill Team campaign - it's from a
BL "short":
http://www.blacklibrary.com/new-titles/new-qu-re/keeler-image.html
The story is about:
I think a very cool/fun base concept and I'm trying to write a campaign narrative for just this purpose using it myself!