Some random thoughts on soft-boiled eggs:
Once upon a time I dated a man who was in the wholesale egg business, a Butter and Egg Man, if you wish. He taught me how to coddle an egg:
In a medium-sized pan with a tight cover put enough water to cover your egg(s) to four times its(their) depth. Bring this water to a rolling boil. Take the pan from the heat, quickly slip in the egg(s), put the cover back on AND DO NOT REMOVE THE COVER FOR AT LEAST 30 MINUTES.
If you have the time to do this you will have a soft, creamy egg, never overcooked.
Again a long time ago, I once traveled from New York City to Sydney, Australia via cargo ship, a 30-day journey. There were only twelve passengers and we had the same menu as the crew, but were served in a different dining room.
One of the most popular breakfast items was soft-boiled eggs. They were served in a covered saucer, without their shells, and were smooth and creamy in texture as in the "coddled" egg method described above. I don't know how the kitchen staff peeled them, as the eggs were very soft and fragile without their shells.
For me, at that time, it was the height of luxury to eat soft-boiled (not poached) eggs that I did not have to peel.