Hard boiling eggs is up for debate

I've been having some issues with my hard-boiled eggs. (YES, this post is going to be about hard-boiled eggs.)
I used to be very confident in my abilities to hard boil eggs, but lately, that confidence has been called into question. I was always taught to punch a hole in the eggs, put them in the water, bring the water and eggs to a boil, let them boil for 10 to 15 minutes, and then pull them out and refrigerate. The 10 to 15 minutes has always been rather vague, but I erred on the side of over-cooked, and went with 15 minutes. But in asking Mom, she said 10.
Lately, the eggs have been really hard to peel, and more times than not, there is a thin layer of egg white that sticks to the shell, and is impossible to remove. The egg white itself, which is the only part that Sydney eats, is thereby lessened because of this. I'm struggling.
Coincidentally, Real Simple magazine published a guide to preparing soft- and hard-boiled eggs this month. In the article, the author suggested a couple changes to my routine. The first change was to lower the eggs into the water when it's already heated to a gentle simmering. The eggs start cooking immediately, and you can start your timing immediately. For hard-boiled eggs, the article says 11 minutes. The rest is eggs.
I tried these directions tonight, and we'll see how they do tomorrow morning for Sydney's breakfast.

p.s. I just did a web search for pics of hard-boiled eggs, and found no less than very many different recipes for hard boiling eggs. Tellingly, I haven't found any of them that advocate the hole punch in the egg shell. Also, they suggest adding some salt to the water to help with the peeling. Also, they say to turn off the burner once the water begins to boil, and let the eggs cook in the hot water for 15 minutes. Then, cool them and refrigerate. That's interesting. I'll definitely try it that way with the next batch. PERFECT EGGS ARE ELUSIVE.