I put a splash of oil in my water. They shells just fall off. I've always ran my eggs under cold water after they were boiled. I didn't see a big difference, but the oil works wonders!
Charlindabob, I am going to disappoint you here. I'm not much of a cook and not nearly as precise about this as you are, but here is what I can tell you:
I have never cooked with a lid on the pan, it has never occurred to me to do so.
Other than some oil I don't add anything else. However I can't really tell you how much oil, because I have never measured it. Probably if you are cooking a large pot of eggs, with lots of eggs, more oil than if you were cooking a small pan of one or two eggs. Egg shells are porous so as they are cooking some of the oil seeps in. It doesn't effect the taste or out come of the egg (that I have ever noticed) but it puts a barrier between the egg and the shell. Those guys just slide on out!
I tend to start with my eggs in the pan and then put the pan on the stove, as I usually break eggs dropping them into an already boiling pan. But I can't tell you if I have seen a difference in the ease of peeling them one way or the other.
I am new to raising chickens, so all of my eggs have been store bought. Perhaps there is where the difference lies. Again, I have no idea. I have heard that "old" eggs are easier to peel, but I can't really tell you how "old" my eggs ever were. As long as they weren't expired I'd use them. Also, because they were store bought eggs they were always out of the fridge and cold.
I also don't know how long I cook them for. Often I over cook them and get that green ring, but sometimes I cook them just right. I'm going to try your 15 min thing. I think I usually did for closer to 20 but I live at some altitude, so I'm not sure if that makes a difference or not.
After boiling them in the oil I dump most of the water out of the pan and run it under cold water. Then I dump all of that out and run it under more cold water. I do this several times until the eggs don't heat the water anymore and let the ones I'm not currently peeling sit in the cold water until I get to them.
Let me know if you like my way, or if it works for you. Maybe you can make it more scientific!
I have been meaning to boil some of the eggs from my girls, so maybe I will do that today and have two pans, one your way, and one my way, and see if fresh eggs make any difference.