Can I make soft cooked eggs in the evening, refrigerate them unpeeled, then heat them in the morning in water heated to, say, 90°F without cooking the yolk?
Poached eggs can be stored in water and reheated the next day for Eggs Benedict for example. Just transfer the cooked eggs to warm water. I've done it for a large brunch and it works really well.
I don't see the point in saving soft boiled eggs in the shell for the next day.
I've taken soft boiled eggs from the night before and taken them to camp the next day to put in a hot bowl of ramen. They warm nicely in the hot broth without further cooking the yolk.