There were a lot of square plates the width of the frame rails bolted to the bottom of the bed before there were custom-fit mounts for goosneck hitches available at three or four shops in every little town.
AS for the idea, I'd say scrap it. You would need some pretty stout tubing to take the thrust from the trailer, the tie-downs and chains would actually do the locating of the ball. The set-up to the reese hitch wouldn't do much, because it can't hold off any side draft. And you have no direct connection of the hitch to the frame.
Why not set up a tow dolly with the hitch permanently fastened to it?