The Japanese captured the Dutch East Indies with their huge oil supplies, early in the war. Fuel only became a problem when they had lost all or nearly all their tankers late in the war.
I agree the Yamato was not supplied with enough anti-aircraft but it was probably not even possible to put enough. The Musashi added a large number of anti-aircraft guns and even they were not enough.
That is why I mentioned she would have to return to the safety of the Lae air defenses. The Lae squadron was the best in the entire Japanese Navy. We would not have risked our few aircraft carriers in their coverage area. The zero had a greater range than our planes too.
I had no idea the Japanese were short on ammo. If so the Yamato could have been an escort for the smaller and older battleships which got beaten eventually by the North Carolina and, I think South Dakota. Night fighting was what the Japanese were best at early in the war.
The problem was that they were constrained in the amount of fuel they could get to the fleet at any one time. They didn’t have a pipeline and they were constrained to their tankers. This meant that for any given volume of fuel, they could have run the Yamato by itself on one mission - or run the entire rest of the fleet on more than one mission. Bang for the buck wasn’t there with the Yamato, and that was the fuel problem. They couldn’t get enough fuel to the front fast enough to get the Yamato to run on regular missions as well as the rest of the fleet.
Musashi didn’t get her AA armament upgrade until late in the war as well, and her end was also late enough in the war that US forces had more than rebounded from Pearl Harbor (1944), so yes, by that point it was irrelevant - but during the Guadalcanal campaign, it would have been critical as at that point we didn’t have the forces in the area to simply throw at an objective until it went away, as we could later in the war.
The Japanese had thought the war was going to be one of battleship duels and had concentrated all of their 18” shell production on AP, star, marker, etc., etc., and had pretty much ignored HE and frag. They had a huge mountain of shells for the Yamato and Musashi... of the completely wrong kind to actually do anything effective for shore bombardment. Even the secondary armament didn’t have much useful and they were not dual-purpose guns.
Also, the Japanese ‘advantages’ at night fighting consisted largely of the fact that their torpedoes worked and ours didn’t. The other advantage was that the US radar at that time was basically useless close in against cluttered island chains and such and therefore was negated - and the Japanese had superior optical rangefinders.