I used a deep socket, the type that has a "seat" inside that holds the nut near the opening. Still a pita. If you had two people it would be much, much easier. Once you have your wrench, drop an ice pick inside the hole to help locate the wrench. Once it is near the opening you can then use the ice pick to center the nut so that the screw drops in more easily.

I thought about rivnuts but was not convinced of their holding power.