I used to put the eggs into boiling water, but that makes the outermost white get tough before the yolk is fully cooked. Never tried using vinegar. The problem isn’t that the membrane sticks to the shell, as Ken seems to think, it’s that the membrane sticks to the egg white and pulls out chunks. Might try the vinegar anyway.
I read your very sad posts about membranes mangling the dang eggs, Hartley. Oh, the toil of this world!
Use this: Add a good amount of salt to your water when you boil your eggs. The shell will remove very easily once you break it. Easy as pie. The more salt used, the easier the shell removes.
May you never struggle with the stubborn sticky shells again.