I'll let someone else comment on the availability of reservations on those days, but we found the leg room to be more than enough in the standard carriages.

I'd say no.

The seats & leg room was fine for myself & my family (including my 6'3" son).

We made reservations (usually just the day before at the train station - at Tokyo & Kyoto in our case) and had no trouble getting 3 seats together in the non-smoking train for times that were exactly what we wanted.

Those two one way legs don't even justify getting a pass, let alone a green one. Are you returning to Tokyo from Hakata? If you're not going to do that then it is best to just buy Nozomi Tickets and save the transit time.

No, we are doing more traveling than that, those were just two legs that were longer as an example.

I had posted more or less the same question a week ago...

There is no green class on the Osaksa-Hakata portion. The Hikari Railstar that you have to use does not have a green class carriage. (The Nozomi does, but you can't use that on the JR pass). So up to you . I have had a green pass before, but on that trip virtually all the trains I used had the green car first class...

Please be reminded that the Hikari between Shin-Osaka and Hakata doesn't contain any green seat. It will make less sense to purchase the green class pass considering the fact.

For your info, the seat configuration in the reserved ordinary carriages on the Hikari running between Shin-Osaka and Hakata, or what is called 'Hikari Railstar' is 2-2, while on the other Nozomi and Hikari trains it's 2-3. The reserved seats on the Hikari Railstar serve as semi green class.

jr-odekake.net/train/…accommo.html

On the link above, the upper left and right, and both of lower images are all of reserved seats. The upper middle one is of non-reserved seats ( 2-3 ).

I suspect you can book seats on the Shinkansen without difficulties for the dates you request. September isn't a peak season in Japan.