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the 'c' notch is the weak point even with the frame boxed. instead of adding a plate to the top in the 'c' notch area. put the plate on the side of the notched area.. and extend the plate a foot or so past the notch going forward and toward the rear. for a plate approx 29" long. i would put the plate on the inside of the frame for appearance sake. that should take care of any issue due to the 'c' notch.
the new hitch in the photo is the right idea... the old hitch can be extended by welding in a tube in the main horizontal tube, then weld in place your extension over the new tubing. so that you have a double wall of steel tubing at the joint seam... i would make the inner tube at least 3" in both directions from the seam you have in the main tube and the extension section... when finished you can clean up the seam weld and after painting no one should be able to tell any work has been done on the hitch...
please post a photo of the '56' f250 towing the dozer....
I was standing in Walmart yesterday near the automotive section when I looked down and noticed a Reese hitch system that is completely adjustable to fit whatever width frame rails you might have. Wouldn't that be the easiest?
I purchased one for a motor home which is adjustable for width. I struggled more to get the receiver height and length just where I wanted it. That turned out to be one made for a motorhome with the adjustable width.