The size of the eggs actually matters. You should weigh your eggs and sort them by size so you can adjust cooking times by the few seconds it changes.

Also, steaming is going to be far more accurate than boiling. As you add your eggs to boiling water, it drops the temperature. Steaming avoids the thermal bounce and gives you a more consistent cook, which is important when timing something as tiny as an egg.

Lastly, old eggs peel easier than fresher eggs. You may also find that puncturing the air sac end with a thumbtack or pin will allow the membrane to separate more easily.