Climbing Mt. Fuji in September 2019 after the official season closes

(Canada)

My son and I will be in Japan in September 2019 for the Rugby World Cup and are planning to climb Mt. Fuji on Sept. 16th via the Yoshida route. We will be attempting to climb the mountain in one day and therefore are planning on an early start. Obviously we will only be making the climb if conditions allow.

A few questions:

- will we be able to drive to the 5th station parking lot? Is the toll road open and will the toll booth be open early (I'm thinking around 6:00 am?);
- will the pay toilets be open and available?;
- do we have to register our hike with the authorities?

Any other pieces of advice would be helpful.