Eggs are a great source for amusement - they are cheap, versatile, tasty (when I don't screw them up too badly), and small enough that you can simple experiments. I also do eat the failures - all though in this case I think I would have preferred not to.
I very much like eggs cooked in their shells for a long time over low temperature. Typically in the 147-148F range. This is sometimes mistakenly called sous vide - it isn't because there is no vacuum involved. Just cooked for a long time in a water bath. As an aside - try putting raw eggs into a vacuum bag....
One royal pain when dealing with eggs like this was peeling them whole. It takes a long time, as it is quite finicky and therefore delays presentation - unless you do them, peel them and then hold them at temp.
I am a home cook, and like things "a la minute" as opposed to being held - again general statement, some things hold really well, but some don't!
So with all that preamble, I thought it would be interesting to try removing the shell before cooking, and still leaving the egg whole. Acid does that pretty well - so into a vinegar bath went the egg.
It takes about 18 hours for the shell to be removed entirely, leaving a little bouncy sack of eggness. So far so good.
Into the water bath at 148 for 45 minutes. It seemed that all was well - the little sac held together beautifully. Quite encouraging, I thought.