Depending on our schedules we color either Friday or Saturday. Put them in the fridge. We always make one for the Easter Possum (see story below). EP leaves basket. In the morning I hide about half the eggs, leave the other half in fridge. We hunt at our house, then in the afternoon we go to my sisters and have another hunt. We have eaten the eggs we use for hiding that same day, and the other half (that's left in fridge) for the remainder of the week. We never have gotten sick either, but may re-think eating the "hiding" eggs. I had a bad bout with a stomach virus a couple of weeks ago and my stomach has on and off bouts with not "being well" ever since.
As for the Easter Possum who comes to our house, when my oldest son was young (he's 23 now) he got up one Easter morning to get his basket and on the back screened in porch, there was a Possum. My son stated the Bunny must have "helpers", and that the Possum must be the helper who comes to our house. We have never changed the story.
We have the boiled eggs for breakfast and egg salad sandwiches until we run out of the eggs.