Wow, that's a long time to boil eggs. I usually do hard boiled eggs for 5 minutes - put the egg in the cold water, bring to the boil, then time 5 minutes. 3 minutes for a soft boiled egg. But then I am at sea level, in Australia, so maybe we do it differently here?
I wonder whether the whites are not setting because the chickens are not eating enough protein. Isn't the setting of the white cooking the protein in the albumin? If they are not eating enough protein, the albumin may not contain the right protein molecules to set properly. Just a thought? Maybe someone who knows more about chemistry can comment further.