i was told by my farmer neighbour not to cut it square / box shape. if the top is narrower than the bottom then the hedge will fill out thicker and the bottom will not go leggy. regular trimming will also help to thicken your bush
you colud alsp try laying the hedge but at 6ft this may be difficult
Hedge Laying
if you are going to add something like an evergreen creeper be careful as this may strangle the life out of your hedge