When I work on a BH, I use my FEL to set it up on its side, then it is no problem to lift the stump jumper up and place it on the splines even with all the blades on it. Just be careful with the blades and pinch points as they will rotate to bottom dead center. A heavy 3/4" drive impact should tighten that nut easily, otherwise you would need to wedge the PTO shaft so it wont turn and use a good cheater bar on a breaker bar to tighten to the closest hole in the castellated nut so the cotter pin will go in.
OH, don't forget to remove the PTO wedge prior to using the mower. BTDT and it isn't pretty when the mower engages.