"Someone on warships1 had the loadouts a while back."
If that's the same thing that I saw, that was an early war balanced munitions load out -- it was NOT the late war bombardment support load out.
"As far as armor a lot of people have the misconception that BBs are armored all over."
Little known fact... the Yamatos were solid blocks of armored steel. No compartmentalization at all...
The US 14"/45 or 50 as outfitting WW I era ships like the Pennsylvania were not capable of penetrating Yamato's side or turret armor at any range, and could only effectively penetrate its deck armor at extreme ranges (30,00o+ yards), or about 15,000 yards farther than any US battleship ever landed a hit.
"Plunging 16/45 was quite capable of penetrating Y's deck armor"
No. The Mk 5 shells weren't capable. The 16" guns on the Colorado-class battleships had only marginally better armor penetration capabilities at all ranges than the 14" shells, which were already deficient against Yamato's armor.
Yes, American fire control radar should help get early hits on the Yamato. I say should given the lackluster radar fire control performance suffered by the older battleship. In effect, that realistically reduces the American advantage of 6 to 1 down to a more reasonable 2 or 3 to 1, unless the Americans close the distance to make visual gun laying more effective.
But, while they're closing the distance to get a better visual fix on the Yamato, they're diminishing the already questionable armor piercing performance of their shells.
"as with what happened to Bismark"
Canard. By the time the Royal Navy's heavy ships got to Bismark she was already crippled and couldn't effectively maneuver due to prior damage from the Swordfish strikes. It's generally pretty easy to hit a target that's going in steady circles and which can't effectively return fire because of that.
Sorry, but no matter how you break this out, the advantage is decidedly on Yamato's size under virtually any conditions.
"that's assuming the Fast BBs don't get in on the action as well."
This entire discussion started with the premise that the PH BBs were going up against Yamato; not the fast battleships.