We need to look at this more closely. The first issue is that it is claimed that PE took ~4 minutes to fire 6 salvos! Really?
2ndly Jasper states that the last salvo fired at PE was unobserved by him because of an order to change targets to PoW. Schmalenbach states that Hood was destroyed just after the 6th salvo landed.
Here's the timing of events as recorded by Suffolk:
Suffolk was not firing nor being fired at and consequently could make accurate notes.Phase 0550 (B) to 0851 (B)
18. 0550 (B). Suffolk's course 220°, 29 knots, following the enemy.
0553 (B). Heavy gun flashes bearing 185°. Half a minute later Bismarck opened fire to port.
0556½ (B). Prinz Eugen opened fire to port.
0559 (B). Hood blew up.
0600 (B). Enemy bore 208°.
If we correct the timing to match PoW's salvo chart we get:
0552:30 Hood opens fire
~0553:00-05 Bismarck open fire (confirmed by Leach, Rowell, Brooke)
0556 PE opens fire
0558:30 Hood blows up just after PE's 6th salvo lands and is witnessed by Schmalenbach.
The KM states that PE received no open fire order from Bismarck but PE's war diary states that PE did receive an order from Bismarck to change targets to PoW. Brinkman must have decided to get into the battle but it is clear that he did so only after Bismarck opened fire.
What seems to have happened:
0552:30 - Hood opens fire (all times as per PoW's AFCT timing)
Lutjens delayed the order to open fire until 0553 causing some anxiety amongst Bismarck's FC team.
0553 - PoW and Bismarck open fire nearly simultaneously.
0556 - PE and Brinkmann opens fire without orders from Lutjens. Somehow the impression is gained on PE that Bismarck did not open fire until 0555 but this is clearly not the case and it seems certain that Bismarck fired first and PE followed her lead.
0558 - PE fires her 6th salvo. Jasper is ordered to change target to PoW. His director moved over to PoW and he doesn't observe the FoS nor does he see Hood explode.
0558:30 - PE's 6th salvo lands and is witnessed by Schmalenbach through the (10.5cm) director.
~0558:35 - a salvo from Bismarck straddles and Hood explodes about 3-5 seconds after PE's 6th salvo lands and is witnessed by Schmalenbach just before he changes the 10.5cm battery target to PoW.
Paymaster Bailey from Norfolk:
Commander Porter from Suffolk:"...I noted in my notebook that "HOOD" was on fire two minutes after she first opened fire, and that she blew up four minutes after that..."
"...The gun flashes started from the port quarter and were immediately followed by gun flashes ahead..."