I have a hunch we are both detail nuts. The three really prime references for the actual sinking of the Bismarck are Duilin and Garzke Axis and Neutral Battleships of WW2, The Final Action by John Roberts, Warship 28 and a follow-up to that article in Warship 1994 that has a superb graphic showing the damage to the wreck of Bismarck on the bottom and identifying the various areas of damage with specific events. It is this last graphic that proves that the armor belt was repeatedly pierced by gunfire. It also has a few surprises - like Dorsetshire's last torpedo hitting the catapult deck. Finally, if you can get to the PRO at Kew, you can get copies of the 1941 DNC reports into the loss of Hood, the sinking of Bismarck and a 1947 addenda to those reports that adds some details not available in 1941. These files also contain the US Navy commentary on the copies they were given.
As to the sequence of fire, Rodney opened the action at 0847. By 0910, (23 minutes later) the action logs of the British ships all state that Bismarck was incapable of further effective resistance. This is the criteria for considering a ship to be silenced. Bismarck did manage to maintain a few sporadic shots after that time, primarily from C and D turrets but D turret was destroyed at 09:21 and C turret got taken out at 09:31. At this point Bismarck gets transferred from the "silenced" category to that of being "dead in the water".
In the good old days, a ship being silenced (the 9:10 condition) was generally regarded as being a perfectly good justification for striking the ship's flag to avoid unnecessary loss of life, hence the stress on being able to maintain an effective defense.
During the action, Rodney expended 375 rounds of ammunition spread by gun as follows AL (36) AC (46) AR (22), BL (45), BC (44) BR (52), XL (44), XC (42), XR (44). In these, the first letter is the turret and the second identifies the left, center or right gun.
KGV expended 339 rounds, spread as follows A1 (22), A2 (27), A3 (30), A4 (32), B1 (36), B2 (40), Y1 (21), Y2 (45), Y3 (37), Y4 (49). the effect of ammunition feed problems can be seen but the ammunition expenditure is interesting in that it shows that the ship maintained a credible output.
Another interesting point is that, although the ammunition allowances were 100 rounds per gun (900 for Rodney and 1,000 for KGV), barely a third of this total was fired off. This suggests that the reported ammunition shortage related more to AP shot depletion. It is also possible that, since Rodney was on her way to the USA for refit, she had been destored. She also had a very inexperienced crew on board.
Rodney and KGV both scored around 40 heavy hits each for a total of 80. The balance of the reported "300 - 400 hits" are 8 inch, 6 inch and 5.25 inch. KGV fired 660 5.25 inch shots, Rodney 716 6 inch, Norfolk, 527 8 inch and Dorsetshire 254 8 inch.
However, the critical hits were as follows. 0859 1 - 16 inch, 0900 1 - 16 inch, 0902 1 - 16 inch, 0910 5 - 14 inch and 1 - 16 inch for a total of 5 14 inch and 4 16 inch hits - nine shells in all. In addition there were two critical 8 inch hits in this period. What is fascinating is the almost surgical accuracy of the British gunfire in this period. Successive hits took out A and B turrets, the primary director, the secondary director, wrecked the bridge and started severe fires amidships.
Photographs of the battleship at 0950 (ten minutes before the scuttling order) shows her very low in the water with her main deck almost awash. At this point she must already have had at least 10,000 tons of floodwater on board and was foundering
According to the action logs, optical rangefinding conditions were extremely difficult due to long range and funnel haze. KGV got an echo with her Type 284, setting the initial range at 25,100 yards and relayed this range to Rodney. Rodney used this range to good effect. KGV accidentally ranged on the radar reflections of Rodney's shell splashes so did not get on target until 0910 when she scored with a concentrated shell salvo. She continued firing under radar ranging using the Type 284 until 0913 when the set broke down. KGVs guns were working OK until 0920 when she started to have safety interlock problems. As a result she started firing salvoes that comprised whatever guns were ready. At 0929, she started using her Type 279 for ranging and did so until 0953 when she returned that set to air search. Rodney fired under optical control throughout.
Overall, KGV had her A turret out of action for 30 minutes due to a shell jamming between the fixed and revolving structures, Y turret was out of action for seven minutes due to drill errors. Five guns out of ten jammed at varying times.
The gunnery problems on KGV and POW seem both to be over-stated. After the Denmark Strait, Captain Leach asked to be court-martialed to dispel allegations that his ship had run away. he was emphatic that he was fully able to continue the action with Bismarck, had every confidence in his ship and was, at the time he was ordered to withdraw, making good gunnery practice on Bismarck having "largely overcome the problems with his guns". He would have to be very sure of his grounds to ask for a court.
Finally, Bismarck's fuel status was really critical. G&D do a detailed analysis which suggests that Bismarck did not have enough fuel to get to Brest after the torpedo hit in her stern - attempting to keep her bows pointing the right way was burning fuel oil in huge quantities. The time the British arrived, the crew had given up and Bismarck was heading NW, away from safety.
In retrospect, that torpedo hit in her stern plus the 14 inch hit from POW seem to have been critical; they sealed the fate of the ship by fuel starvation and steering damage. All the sources agree that the scuttle order was largely irrelevant - G&D describe it as being nothing more that a routine part of the process of abandoning ship.