My family and I (3 people) are traveling to Japan in September I recommend you prepare for bad
weather conditions.
Flights are more liable to be canceled due to strong
winds.
During the typhoon season, I don't count highly on flying.
I suggest you plan to take
one HIKARI train and one HIKARI or SAKURA train,
allowing at least 30 minutes for a transfer at Shin-Ōsaka.
NOZOMI trains connect Tōkyō and Hakata directly.
If you take two trains, a transfer at Shin-Kōbe would be easier.
Still, it may be better to split your route at Shin-Ōsaka, I think,
considering that trains from Tōkyō,
when there is torrential
rainfall along the course,
might be suspended beyond Shin-Ōsaka.
As long as you are inside the Shinkansen zone,
you can pay the Shinkansen surcharge for the entire route;
make sure to book the two train rides together at once.
I thought that with over sized bags you needed to have a reservation? Yes.
You see the introduction by JR-Central.
- JR-Central: Reservations for Seats with an Oversized Baggage Area
https://global.jr-central.co.jp/en/info/oversized-baggage/