Outside of 25,000 yards and over the horizon the Missouri can connect with its state of the art radar fire control. If the battle is fought at this range the Yamato is not going to score hits and that infernal radar will remain intact. (Ditto for a night battle, so 12 hours out of a given day, the Yamato loses.) At extreme range the worst the Missouri can do is a draw.
Here is how I would try to use the Yamato to advantage:
I would launch my full complement of aircraft, gaining air superiority for gunnery spotting. I would push the BB’s powerplant for every bit of speed it could muster and head directly for the Missouri. My objective would be to close within 25,000 yards where my optics based gunnery should be sufficient to score hits on the USN BB.
The problem is that the Missouri’s skipper isn’t going to sit there waiting for me to close the range. He’s going to be firing even outside my visual range, perhaps with broadsides. This is where my aircraft help. I will have them announce each salvo so that I can perform a prompt heading change each time. There is sufficient travel time at long range for this to be effective. This is costly though as it reduces closure speed toward the enemy. The alternative would be to head straight in without evading…but I don’t think Yamato’s decks, fire control, and the like will survive the punishing 2700 lb APC rounds falling from steep angles.
As my opponent begins to appear on the horizon I’ll begin firing my forward guns, attempting to time the salvos to just before the Missouri fires (this of course relies on timing the roll rate as well), then alter course again. Hopefully, this will succeed in getting off a salvo 2 out of 3 times for every time the opponent fires. It will also allow some honing of the aircraft assisted spotting.
If I make it to 25,000 yards without suffering a critical hit, I will begin relying on a shallower approach angle, so that I can bring all three turrets to bear. If I score a hit I will maintain course and fire rapidly, willing to take a hit while I have a good firing solution. If I notice the opposing gunnery is becoming erratic I will assume that their fire control/radar is damaged, and I will stubbornly maintain course, firing broadsides.
If somehow the fight continues without one of us suffering grievous harm, I will be trying to reach about 15,000 yards where my 6.1" light cruiser turrets should be reliably connecting. The hope is that they will cause enough havoc to knock out some of the command and control or the 5" turrets. At this range, I would expect the Yamato to have a decisive advantage from the main battery assuming my fire control is still essentially intact.
If on my long approach the Missouri turns away, I’ll willingly exchange blows with my 2 forward turrets against her aft turret.
Of course, the problem with this is that I don’t have the initiative, the commander of the Missouri does. Having more advanced technology and a much faster ship gives the Missouri standoff capabilities. Her skipper will dicatate what range the battle is fought at.