I know it's only a wikipedia reference but this:
https://en.wikipedia.org/wiki/Japanese_battleship_Yamashiro#Battle_of_Surigao_Strait seems to indicate West Virginia first hit Yamashiro @ ~22,700 yards, with Tennessee and California joining in shortly after... Not quite as good as Warspite and Gneisenau, but I would be inclined to judge their gunnery as "competent" at long range.
This here is the more accurate report, showing the USN Battleline had many problems in rangefinding and engaing Yamashiro, mostly due to their own activities:
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At 0351, when YAMASHIRO, MOGAMI and SHIGURE were 15 600 yards (14.2 kilometres) from Oldendorf and Berkey’s cruiser, Oldendorf ordered both cruiser battle lines to open fire on the three Japanese ships. RADM Oldendorf’s is quoted in his after action report; “Every ship in the flank forces and the battle line opened up at once, and there was a semi-circle of fire which landed squarely on one point, which was the leading battleship. The semi-circle of fire so confused the Japanese that they did not know what target to shoot at.” Over the next twenty minutes Oldendorf’s ships and men, including many Pearl Harbor veterans, gained their revenge, 3000 heavy projectiles, including 14 and 16-inch shells, slamming into and around the three Japanese ships.
For Nishimura, after the PT Boats and the destroyer attacks, there was nothing more he could do. One moment in front of him there was nothing on the horizon, either visually or on the fire control radar which by now was affected by multiple returns reflected off the land on either side of the strait to be effective, the next moment the horizon lit up as Oldendorf’s heavy ships began their attack with full broadsides. That was at 0352hrs, and Nishimura ordered FUSO to make best speed, not realising that FUSO had just blown up several miles behind him. Nishimura’s final order to his battered fleet was; “You are to proceed to attack all ships.”
YAMASHIRO by this time was at 12 knots and engaging targets visually as the battleship became the first target of the cruisers. DENVER opened fire, followed by PORTLAND, COLOMBIA, LOUISVILLE, and MINNEAPOLIS.
The battleships were now passing ahead of the enemy column in the classic crossing the "T” manoeuvre. WEST VIRGINIA, with the latest Mk 8 fire control radars, opened fire at 0353hrs on YAMASHIRO, firing ninety three 16 inch before stopping. Shortly after the first salvo reached the YAMASHIRO, killing Vice Admiral Nishimura. The cruisers PHOENIX, and BOISE then joined in, targeting YAMASHIRO, with RADM Berkey informing BOISE to slow her rate of fire to conserve ammunition.
At 0355 TENNESSEE and CALIFORNIA opened fire, the two battleships firing six round salvos from their main guns, one hundred thirty two 14-inch shells were expended between them before they too stopped firing. The three remaining battleships, MISSISSIPPI, MARYLAND, and PENNSYLVANIA, with older fire control radars, were having trouble getting range.
The nine destroyers of DESRON 56 entered the battle. Between 0354 and 0359hrs six destroyers launched over twenty torpedos at ranges up to 8000 yards (7315 metres) without success then withdrew under fire.
SHROPSHIRE was having trouble with her fire control system, and as she, along with PHOENIX, and BOISE conducted a formation turn towards the west SHROPSHIRE finally opened fire with her 8-inch guns at 0356hrs. SHROPSHIRE’S Commanding Officer, Captain Nicholls in his after action report stated “A very high rate of fire was attained in rapid salvoes; as many as eight broadsides in two minutes being fired.”
For the DENVER another target came into view, and she shifted fire to SHIGURE at 0358hrs, and continued to fire. By now the range had decreased between Oldendorf’s heavy units and the YAMASHIRO, MOGAMI and SHIGURE, and as the fire from Oldendorf’s ships increased in accuracy the three ships to the southwest as they began to withdraw. YAMASHIRO and MOGAMI had suffered moderate damage while concentrating their fire on the closest US cruisers, while remarkably the SHIGURE had only received one hit from a dud 8-inch shell.
At 0359hrs the battleship MARYLAND, using the WEST VIRGINIA’S fall of shot (and the large columns of water they created) engaged, firing 48 rounds. MISSISSIPPI’S fire control radar only allowed one targeted salvo against the three ships, while for the PENNSYLVANIA, her fire control radar refused to lock onto anything and was the only battleship not to fire a shot.
MOGAMI had taken heavy damage, and while the crew raced to repair damage all over the ship the MOGAMI fired torpedos at the incoming destroyers of DESRON 56. That was the last attack MOGAMI made as the cruiser PORTLAND fired a salvo of eight-inch shells at 0402hrs at MOGAMI, hitting the bridge, killing her captain, as well as hitting the engine room and bringing MOGAMI to a stop.
For the remaining three ships of DESRON 56, USS ALBERT W. GRANT (DD-649) USS NEWCOMB (DD-586) and USS RICHARD P. LEARY (DD-664) they began their attack at 0404hrs while the battleships were engaged. After the three destroyers followed the YAMASHIRO, and paralleled the battleship after she turned to the southwest. At 6200 yards (5669 metres) RICHARD P. LEARY, NEWCOMB and ALBERT W. GRANT launched thirteen torpedos at YAMASHIRO.
The ALBERT W. GRANT was then targeted by the YAMASHIRO and was fired on during her attack, scoring several hits. Eleven shells fired from an American cruiser then hit the ALBERT W. GRANT, believed to be fired from DENVER, who had mistaken the destroyer for SHIGURE. 34 sailors were killed, 94 wounded. As word of the friendly fire incident reached RADM Oldendorf at 0408hrs, he ordered all Allied ships to cease fire, to allow the destroyers to withdraw. NEWCOMB came to the aid of ALBERT W. GRANT, and together both ships sailed out of danger.
As the order to cease-fire came through the MISSISSIPPI fired a broadside at 19 700 yards (18 kilometres) at the retreating Japanese force. This became the last salvo fired in a battleship vs battleship action. As the distinguished American naval historian, RADM Samuel Eliot Morison, wrote of the battle,
“In the unearthly silence that followed the roar of Oldendorf s 14" and 16" guns in Surigao Strait, one could imagine the ghosts of all great admirals, standing at attention to salute the passing of a kind of naval warfare they all understood. For in the opening minutes of 25 October 1944, the Battle Line became as obsolete as the row-galley tactics of centuries before.”
DESRON 56’s nine destroyers fired multiple torpedos during the attack, but two from NEWCOMB hit Nishimura’s flagship at 0411, stopping her dead in the water. The torpedo hit, on top of the damage inflicted by the cruisers and battleships, was too much for YAMASHIRO, which rolled over, sinking at 0419hrs.
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Starting range was 15,600 yards and closing, not the 20,000+ yards suggested. Hits were mostly scored by the cruisers of Oldendorf and only three BB's actually engaged her directly, scoring a few hits at a flat trajectory. Torpedoes were the killers on Yamashiro, taking two prior to the engaging Oldendorf and two more, which put her down in the later stages of the engagement.
So Oldendorff's BB line did help to create serios damage, but not cause the loss of Yamashiro. Destroyers were the instrument of her destruction, with, or without the support of the BB's.