Trying to think outside the box. Since the hangers have to lift up you need to find a way to prevent them from lifting too high.
My first thought is maybe an appropriately sized piece of plywood that lays flat across the top of the files and fill the gap. When the drawer is closed the files can't jump up to unhook. When the drawer is open just remove and set the piece of plywood on the floor to get it out of the way. Thinking further the plywood probably doesn't even have to be thick enough to fill the gap between the hooks and the top of the cabinet. The weight of the wood alone might be enough to keep the hooks in place.
