when you find out the problem let me know!!!!
we are going through the same thing, and have been for the last few months. we've replaced the ballcock and the whole arm piece that it sits on, adjusted the kitchen sink as that's what seems to set it off, and STILL it overflows
the water flows out the pipe which sticks out the side of the house but the water that sits on the ceiling floor leaks through the ceiling in the hallway. so now we have a rooted hallway and watermarks on our new carpet
FIL is coming over this weekend to have another go at it, probably end up bypassing the header tank in the roof altogther.