There is a nice book called Ocean Flying, written by a female ocean ferry pilot, who frequently ferried single engine a/c across the Ocean. There are lots of nice stories in it.
One surprising remark was she was often more confident flying single engine a/c across the Atlantic than twin-engine a/c. Her observation was that most of the light twins she ferried could not maintain altitude with one engine out and a heavy oceanic full load -- so the 2nd engine was not actually much of an extra safety benefit. She also observed (though admitted she did not have scientific evidence) that the twin engine aircraft seemed to have so many more engine problems. (Certainly training twins tend to have more engine problems due to the amount of time engines are abused doing engine failure training perhaps.)
She has a bunce of nice stories in the book. She recounts how a friend of hers accompanied her on a trip. He was a 30,000 hour 747 captain - however he was unable to fly a real plane. He was unable to concentrate on flying a course straight and level for more than a few minutes as he'd spent so long flying autopilots. On several occasions she discovered they were as much as 90 degrees of their required course.
There is lots in the book about preparation for a ocean single engine flight - HF
radios, nav equipment, exposure suits, emergency beacons, food, toilet etc. I recall Transport Canada has some staff in Goose Bay that check out a/c intending single engine transatlantic flight. They regularly have pilots arrive from US and Canada intending single engine crossing without the vaguest idea of the suitable level of equipment to ensure their safety.