I've never done limousine in Jpn. But there's the limousine bus (just a regular highway bus; they take care of your luggage for you), which is door to door but very limited in frequency on your route.
http://www.limousinebus.co.jp/en/pla...hes/index/4/57

There're also taxi companies that you can pre-book with flat rates to different parts of Tokyo area. One is MK Taxi (http://www.tokyomk.com/eng/airport.html). MK seems to do limousine service also, but I've never used it.