"14.3 WARDS Some abilities allow you to roll a dice to negate a wound before it is allocated to a model. Abilities of this type are referred to as wards, and the dice roll is referred to as a ward roll. Up to 1 ward roll can be made for each wound or mortal wound before it is allocated to the model in question. If the ward roll is successful, the wound or mortal wound is negated and has no effect on the model."
"Q: Some abilities allow you to roll a dice to attempt to negate a wound or mortal wound, but that roll may have a different effect depending on the score of the dice (as per, for example, the ‘Soul-forged Guardians’ ability on the Praetors warscroll). Are these abilities wards, and is the roll a ward roll? A: Yes."
"Morikhane: This ensorcelled armour protects Nagash from arcane as well as physical attacks, and can even cause an intense magical backlash on those that dare strike him. Roll a dice each time you allocate a mortal wound to this model. On a 1-3, nothing happens. On a 4-5, that mortal wound is negated. On a 6, that mortal wound is negated and the attacking unit suffers 1 mortal wound"
No where in the core rules or FAQ does it state you must use your best etc, as the controlling player you would have the choose of which you would take therefore can pick 6++ deathless save for the best chance to trigger Protection of Nagash. However Morikhane does not state may, so taking the 6++ instead of the 4++ is the best you can do in this case.