Now that I understand the application that is easy to do with a little compromise.
Use these. Put the angle of the left under the existing platform, perhaps right where the existing hinge is located now. Bend the other leaf flat and bolt to the outside of the gate. When it folds 90º you will have the distance between the leaves less the thickness of both floors.
Another style of offset hinge:
Or, if these will allow you to flip the center leaf: (they should)
