Just a thought you might consider when you fab your hitch.
I made a hitch for a 84 chevy school bus a few years back which of course has a high rear bumper.
I made it to have a receiver so the hitch would barely show and not hang down to the height needed for the trailer.
I got a beefy 8in drop receiver to use when I wanted to tow which brought the ball down to the correct height.
I know the hitch is going to show on a flat bed, but using this idea will at least minimize what has to hang down from the frame and possibly look better.
Dan