I was on the 14 night Eastbound cruise in 2005, and also travel from Europe so have the luggage issue 'double' with transatlantic flights.
You have to be economical with what you take, plan in advance, often people take too many things.
Now the laundry's are very busy indeed, cruisers think with so many sea days it will be less of a problem, but as it is a long cruise, everyone thinks the same, cut the luggage and wash on ship, 2/3 times during the cruise.
All laundries were busy on Panama crossing day! we went to all at 6.30am, all full, people said it had been full all night?. Everyone thinks Panama day, all will be watching the transit, but actually lots of people were washing their smalls.
I would suggest keeping an eye on laundries, maybe port days if you get back early, this was successful for us in the Med on an 11 night cruise. We came back from Rome quicker than expected and was able to walk straight into the laundry and it was empty.
If staying anywhere before the cruise, IE
Disneyland wash there on last night.
Use tux hire formal wear hire to help that cuts down on your luggage.