The method that has worked the best for me, even with fresh eggs, is very similar to the OP's, but this method boils for 13 minutes. The two things this method calls for, and something I've not done in the past, is to add the eggs to boiling water, and then peel them right away after they've been in the ice bath.
I got this method off youtube:
•BRING POT OF WATER TO BOIL FIRST
•TAKE EGGS DIRECTLY FROM REFRIGERATOR
•PLACE EGGS IN POT WITH LARGE SPOON/LADLE
•BOIL FOR 13 MINUTES EXACTLY
•REMOVE FROM HEAT AND RUN COLD WATER OVER EGGS FOR ABOUT A MINUTE.
•NEXT COOL DOWN EGGS WITH ICE AND LET COOL FOR 15 MINUTES
•PEEL EGGS IMMEDIATELY