Can you suggest other ways to get mountain hut reservations?

by Julia
(U.S.)

Your website is full of valuable info.

I asked a friend to call all the 8th and 7th station huts for the days I can climb (July 28, 27, 29) and nothing is available for 2 adults and 2 children (9,11). We are so looking forward to summit at sunrise but with young children I am afraid we won't succeed if we don't get a little rest.

Can you suggest other ways to get reservations? Tour companies hold spaces, but we are traveling independently and will arrive at Mt. Fuji from Osaka, not Tokyo.

Are there other sources? Please help. Thanks in advance for any advice.

Julia