The trailer hitch that didn't fit has been returned, and one that does fit is installed. Draw-Tite #41001 is the correct part number if anyone is looking for a class IV hitch that fits good. It drops 5.5" for bumper clearance and sticks out about 10 inches from the end of the frame.
This truck is now ready to tow better than ever, and the search for a little classic travel trailer begins!