Re: Generous police
Manslaughter is enough to keep him in prison while they investigate. He's admitted she died in an "accident" on board. The "burial at sea", sinking, and lying / change-of-story are certainly suspicious and at minimum the police can say they suspect the accident was his fault. That's enough to charge him with manslaughter and hold him for a bit (perhaps until trial), and it'd be very hard for him to contest that given what he's already said.
If/when they get evidence of other crimes then they can charge him with those, but there's no rush. (E.g. they might suspect him of murder, hiding a body, and attempting to frustrate the investigation by deliberately sinking his submarine).