Set fare taxi Haneda to Yotsuya

Hi

Thanks in advance for your help.

We are a family of 5 (3 young children) arriving in Haneda on Thursday morning at 5.05am. We plan to go to our hotel in Yotsuya (Shinjuku) straight away and leave our bags.

My questions:
1. Do the set fare taxis accommodate our family of 5 plus a driver?

2. How do I go about booking it?

3. What if my plane was delayed, would this cause big dramas?

4. Does it take long to get out of Haneda Airport, through customs etc? Should I book it for a lot later to allow for this?

5. Is this the easiest way to go or should I just get the limousine bus and train?

Thank you
Michelle

This one claims to be cheaper than taxi :

http://www.tokyoairporter.com/?gclid=CPrx_faqmcsCFVMIvAoddVcPWQ

Do the set fare taxis accommodate our family of 5 plus a driver?

Well, if the three kids among you are small enough, one medium-size taxi car may carry you the five passengers.
Or, if any of the three kids cannot sit on the parent's lap, you may need two taxi cars.

The one-way fixed-rate taxi fare to get from HND to Shinjuku (during 05:00 - 22:00) is set at 6800 yen per car; when the driver takes a toll road, you should pay also the toll.

How do I go about booking it?
What if my plane was delayed, would this cause big dramas?

In a case where you don't appear by the time which you have indicated, a waiting fee mounts up rapidly.
So, I recommend you would not book a taxi with a pick-up time specified.

Does it take long to get out of Haneda Airport, through customs, etc.?

That may depend on the crowdedness, but usually one hour seems to be enough.

Is this the easiest way to go or should I just get the limousine bus and train?

Well, if each of you five travelers has got accustomed to taxi rides, it may be the easiest way.

Personally I don't mind having a few train rides and walking a little in order to save my transportation cost.
I guess you can get to Yotsuya Station by rail before a peak of the weekday morning rush, unless your plane is delayed by more than 1 hour or your immigration procedures need more than 1 hour.

Which station on which line is located close to your hotel?
When in the year will you come?