Gatwick is still stuck with the same problem of having to cross a live runway to get to the southernmost!
Not necessarily.
The schematic layouts in the proposal don't show any taxiways, but they do show the airport boundaries being extended to both the east and west as well as to the south.
So it's quite possible that an end-around taxiway could be provided at either or both ends of the current 08/26 to obviate the need for runway crossings.