I have a 15.5 gallon keg that I boil up to 14 gallons in which is quite full, I'd imagine about about as full as if you had 12 in yours.
Get a spray bottle and set it to mist. When you get it to start boiling drop you heat down on your burner, and spray the foam on one side of the keg. Then you can slowly raise your temp till you get back to a good rolling boil. Just remember to spray the same one side when the boil starts to foam up. I know it sounds weird, but what you are doing in starting a convection current, the cold spray causes the wort to fall to the bottom on the side you are spraying and is setting up a current that pulls the foam back in to the kettle stopping boil overs. I takes a little practice, but I have found it to work really well. And when you get a good current going you can really see it working.