I realized this doesn't apply to the OP anymore, but there have been times when I arrived at NRT that the Limo Bus going to the Park Hyatt may have just left with a 20-30 minute wait time.

It is worth knowing that there is also a Limo Bus to the Shinjuku Washington Hotel that is a short walk from the Park Hyatt (unless you have more luggage than you can carry.)

I saved 30 minutes of waiting at NRT doing it this way the last time I was there.