I think you are referring to the Deep River Southern type box that pivots on a center screw. I have not made one of these, but have done some study on them. The ones I've been able to get good a good look at, seem to use a spring catch in the box that engages a notch in the cover. I have not had a chance to examine what type of opening spring they use, but I would consider a flat spring that puts pressure on a post attached to the lid, that uses the recess in the stock as the stop to prevent the cover from spinning to far around. Maybe somebody else has had a hands on experience with this type box. They are fairly rare.
Hungry Horse