Larry, if I understand your proposal correctly, it seems to me that your idea would create an inverted wing cross section that would generate downward lift, counter to the main wings. Also, any parasite drag reduction the fairing creates might be replaced by induced drag, both from the downward lift of the fairing and from the increased wing lift required to offset the fairing lift.

Just thinking out loud here. I could be out to lunch; as I have proven in multiple forum posts, I am not an engineer!