I'm doing the same cruise as I'm equally boring I wouldn't mind joining you for the odd excursion providing your son hasn't got any nasty teenage habits.
From the dock you can actually walk to Piazzale Roma - it is probably about 12 mins hauling luggage - or there is a cab rank right outside the dock who will run you up there for a few €. Make sure you get into a registered metered cab though. Have you checked on cruise critic to see if there is a roll call for your cruise to meet up with fellow travellers.
We have travelled on Costa six times and the disembarkation procedure is very efficient. There are buses from the ship to Piazzale Roma on a continuous basis and the journey is only 5 minutes but DO NOT walk with the luggage it is not as easy a journey as the previous answer suggested. Costa also say in their disembarkation briefings that if you have a connection to catch to let the reception know and they will then give you a RED colour sticker - which is the first off the ship. We did this journey last week, had a red sticker and easily met the schedule times you have.
By the way Costa are excellent and you should have a great time.