Never had trouble with this until 2 years ago we moved to 7,000 feet.
Now, I did my research and learned that the "solution" was: older eggs, salt the water, figure out the timing by trial and error.
So, OK, my eggs are cooked the way I like them: quite orangy-yellow rather than yellowy-green (when they're overcooked).
But, no matter what I've tried, the shell doesn't lift off the egg white...it sticks and it takes forever to peel and/or pulls off hunks of white making the egg unsuitable for presentation (ok for chopping in egg salad)
Frankly, I'm suspicious that it's the hens and that some are genetically prone to sticky shells, but I've tried inexpensive supermarket eggs, eggs from hens with more room to roam than most humans, with anti-biotics and without, organic and loaded with chemicals...the results are the same.
I've conquered making rice at 7,000 feet and am not into baking (that must really be a challenge).
But, I do eat a lot of eggs and I'm SURE one of you can help!