Second take: USS North Carolina is teleported back in time from Nov 1941 to May 1941, wih Mark3 radars and CXAM-1 radars on board.
Due to her range at 25kts being very close to Bismarck's range at 24kts (10500km for NC at 25kts vs 12000km for BS at 24kts), I think it is feasible for her to go at 25/26kts on the same projected track Bismarck had.
Thus, NC would move on the same timeframe: May 23rd 19:30 - discovered by Norfolk; N.C. shoots at the cruiser, which escapes in the fog banks.
May 24th 5:45 - British capital ships are seen, but not immediately identified. Luejtens helds fire from the 9x406mm guns until 5:55.
N.C. crosses the T of Hood and PRince of Wales. Allthough her guns have a steeper trajectory then Bismarck's, N.C. strikes Hood 2 times, causing a catastrophic and immediate destruction at 6:00. She then ponds heavily on Prince of Wales - who withdraws under smoke.
However, N.C.'s forecastle is hit, as well as her internal belt , adjacent to the machinery room. Still, the internal belt of 150mm stops some of the damage, except the force of the blast which was directed beneath the internal armor belt.
Some flooding occurs - both in the forecastle, and in the machinery room, as well as in the void between the outer hull and inner belt.
N.C. loses 2-3kts of her max speed, and speed is reduced to 20kts for the moment. Temporary repairs are done over the day.
In the night, 8 Swordfish bombers attack the ship. Her AA guns (16 x 28mm, 20x127mm, 12x12.7mm) was only marginally more then Bismarck's original armament (16x37mm, 16x105mm, 20x20mm). Thus, even if she would shoot down 1 Swordfish, I doubt she would cause enough damage to the others to escape the 1 x torp hit amidships.
The hit will further reduce speed by 1-2kts, and cause some local flooding, but not much. Probably the shock of the expplosion would cause immediate shock damage trroughout the ship (but smaller then the one suffered in 1943 due to 1 x long lance torpedo), which would require reducing speed for 2-3 hours for repairs (something Bismarck was not required to do).
This in turn would offer Tovey invaluable time for KGV/Repulse to home in. As Suffolk wouldn't be losing radar contact anymore, she could direct the heavy ships through the night.
As day would approach, repairs would be complete, and Luejtens would attempt to avoid the radars, but it would be ~ 5:00AM, and Suffolk on another search leg, and KGV at only 50 miles to the N-W.
As first rays of light would appear, N.C. would lose contact with Suffolk , but KGV would be moving south, and be in intercept pposition by 8:00AM.
If interception occurs, N.C. would fight at ~ 18kts versus KGV and Repulse coming at 27kts. She would cause damage, but would eventualy lose , and be torpedoed by the escorting DDs and sunk.
If interception doesn't occur, N.C. would continue to travel at 18kts towards Brest.
She would be discovered on the morning of May 26th, and try to increase speed to 20kts (BS increased to 25kts).
Heavy ships would converge on her, along with Ark Royal. Torpedo bomber strike would come around 20:30, and hit with 2 torps - 1 in the stern, 1 amidships beneath the armored belt, blowing another hole in the hull, but with the force of the blast being contained by the inner belt. NOnetheless, significant flooding occurs, and the ship slows to 10kts as it is doing repairs (rudder still operational) , and it is intercepted by Sheffield and 5 DDs.
In the ensuing battle, NC damages several enemy ships, but can not increase speed above 12kts due to flooding.
In the morning, KGV/Rodney start attack head on. She responds with 6 main guns forward, which are silenced at 8:58.
The bombardment continues and N.C. explodes in several places due to magazine (secondary magazines) explosions. At around 9:20, a 16" shell perforates through the inner and through the main barbette, exploding inside the main elevator and causing a downward and upward vent of explosion which devastates the forward part of the ship. N.C. remains dead in the water , as Rodney, Dorsetshire and several DDs launch torpedoes. She sinks at 9:40 at ~ 1400km west of Brest.