How far in advance do we need to book the Mt. Fuji mountain huts?

by Jamie
(USA)

Hi Gary, firstly, great website! Thank you very much for the effort you've put in to it!

I was just wondering rounghly ​​how far in advance we need to book the mountain huts?

We're arriving in Tokyo on 17th July, and intend to climb via the Gotemba route on 21st July, saying in the 7.9 mountain hut. Though with an entire lack of Japanese, I'm struggling to understand exactly when I can book, and have a feeling language might be a barrier to booking at all. Will we be ok to wait until we are in Tokyo and asking our hotel to book it for us? Or will that likely be too late?

Thank you!

Jamie