Assuming I start with fresh eggs, boil them until they are hard enough
to slice with a household egg slicer, and refrigerate promptly, how long
will they last?

I seem to recall a restaurant I worked in many many years ago kept them
peeled and in water in the walk-in, but that was prolly just for ease 0f
use when needed... but...
Would they last longer shelled or unshelled.

Any egg longevity experts out there?