I think the airport-to-airport shipping option is the best, as has already been discussed. But as a point of order, I wanted to mention that the above prices are no doubt for a chartered van arranged by the hotel in advance, like a limo. You can get a metered taxi for less, and some taxis are vans. At the airport, if you go to the taxi stand and tell them you need a van, they'll probably be able to send one to the front of the line. On the way to the airport, the hotel should be able to call the taxi company and schedule one in advance.

Since the taxi vans are just metered taxis, standard fares apply. Narita to central Tokyo should be no more than $250, which is less than half what a charter through the hotel would cost.