Connection from HND to JR to Fukuoka

Arriving HND at 2:20 pm on Sept 6 and want to use a JR pass to get to Fukuoka. Will I have enough time to clear customs and get to the train before the last train departure of the day? If I pay for a greeter at the airport will this speed up the process. I'm having trouble understanding the train schedules.

Hyperdia.com

Start = haneda
End = hakata
Time = after 3:20pm

Yes.

It will take extra time to exchange your JRpass voucher and do reservations, so rather than a 3:20 departure I would suggest 4:00 - you might leave earlier but it will not make much difference as you will be aiming for the 17:10 Hikari 481. You might get an earlier Hikari, but for the connection with the last Sakura service of the day it's not going to matter as that is one hour earlier.

Not sure what is confusing about the timetables.
Haneda to Shinagawa. Hikari to Shin-Kobe and then Sakura to Hakata. A little over six hours. Arrival 22:52 p.m.
Note reserved seats on the Sakura Service do sell out so you might be in a non reserved car (either sitting or standing).

Thank you. I think we've decided to fly to Fukuoka from HND instead of trying to catch the train. My wife has never been to Japan and she will miss most of the scenery since it will be getting dark around 6 pm. We'll take the train back to Tokyo during the day for the scenery. Any suggestions on which local airline to book with out of HND? I imagine it will be in another terminal so we'll need time in customs and time to get to the correct terminal (we land at 2:20 pm +/-).

I think flying is the right decision, unless you decide to spend the night in Tokyo & travel the next morning. Unfortunately as it's a Friday afternoon flights will be more expensive. You are correct that the domestic flight will be in another terminal but there are buses & the monorail between the two. I have done the connection in 50 minutes but that was with help from the JAL staff and I only just made it. If you allow an hour and a half you should be fine. Just have your things ready to go through security again. I had a single ticket from London to Fukuoka so I can't really suggest which airline would be best.

I would choose to fly - you're already right at Haneda Airport, and Fukuoka Airport is right in the city when you land there - 5 minutes by subway to Hakata Stn and just a bit more to Tenjin.
ANA has some excellent fares on its Experience Japan Fare.
http://ana.ms/20Xtf8t
and JAL has its own clone of it.
You don't give any further itinerary, but Kyushu offers a lot. Fukuoka has some good sights as well, but not as well known.
http://www.thejapanfaq.com/fukpic.html
https://goo.gl/X3LDaE

And to put in another vote for flying, depending on your particular route, the scenery can be quite nice from the air. I've not flown to Fukuoka so I am unsure of the routing, but we just flew Narita to Itami and got a great (and our only that trip) Fuji-san view from the air.

Honestly, unless you're hoping to see Mt. Fuji I personally don't think the Hakata to Tokyo shinkansen route is as scenic a train trip as some other train trips in Japan It's a lot of cities.

Before you fly - don't forget to check out the JAL and ANA explorer passes which are normally around 10,000 yen to many locations in Japan. a budget airlines might be cheaper

Wow, thank you for all the great information, this is really helping to answer so many questions! ANA has a 5 pm flight to Fukuoka which should give us plenty of time if we land at 220 pm, clear customs, and change to terminal D2. Only $105.00 each using the Explorer Pass. Next question - Which side of the plane should we sit on if we want to get a good view of Mt. Fuji?

You are welcome. Have a great time.

Haha.. The right side. The plane will be full of people who do this trip often and don't care.