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Have you tried Classic Haulers Home - Classic Haulers F-1 Parts. Give them a call, they have things not listed on line and are very helpful, if they don't have them they may be able to tell you where to find them.
If you want used, stick around, there are a number of members that have parts stocks.
I was wrong about the size, I measured the square holes and the one in the bracket is 3/4 x 5/8 and the bumper is 5/8 square. The 9/16 would work but would be a little sloppy I believe. A 5/8 carriage bolt will fit the bumper perfectly with a little room for sideways adjustment in the brackets.
Rezvani's Latest Post-Apocalyptic Monster Is a Ford F-150 Raptor Underneath
Slideshow: Called the Fortress, the 850-horsepower pickup combines Raptor underpinnings with military-inspired features, survival equipment, and a starting price of $285,000.