Thanks for the comments. I asked something similar on an RV forum which I frequent. Someone pointed out this hitch.
It is similar to what I was imagining. Mine would have been taller. However towards the end of the video we can see the problem with a bed cover is really the hardware on the trailer side. The pinbox and pin are too far down below the trailer. In conventional use, the flush lower surface of the trailer in the hitch area is about 6-7" above the pickup bed rails. My idea would require that the existing pinbox be reengineered from the frame down, not just replaced with a short gooseneck hitch.