Hi bizzybee. As you are going on Millennium, leave the laundry detergent at home as there are no self-service laundromats. (Great idea, though, rochbie!)
We used Celebrity's laundry service on Century and were very pleased with it. During the cruise, they ran a special for something like $20 for all you can fit into a large paper bag they supply.
As to the packing question, take it from someone who lives in the Northeast -- layers are the way to go. Your list sounds fine, but you can cut down on the bulk by bringing just one or two sweatshirts, one fleece jacket, and perhaps a windbreaker to wear on top any or all of these items in case of rain. (This is what we packed for our cruise to the Norwegian Fjords earlier this year.) Same for the jeans -- bring a few pair, and have Celebrity launder them as needed. We were able to stuff 2 or 3 pair into the $20 bag mentioned above.
What types of excursions are you planning?