Mt. Fuji hut reservation – is it competitive?

Hi everyone, forgive me, I’m posting on my mobile for the first time!

I’m am traveling to Japan to visit my nephew. My plan is to travel by myself the first week and meet up and travel with him my final week when high school finishes. He has told me July 28. The week before that I am wanting to climb Mt Fuji. I have done my research and read a lot here (thank you so much) but my question is will it be hard to get a reservation to a hut for the end of July??? The mountain huts are just opening, school is still in session, etc.

The reason I ask is I will be away from a computer on April 1 – the day reservations open and fear I will miss out on my specific day. I am from Canada and when reservations open up for huts and camping spots to our National Parks there is so much traffic that it crashes computer systems and it’s literally a lottery if you get a reservation or not. Reservations for the season are claimed within minutes. If you’re curious look up Moraine Lake reservations or Lake O’Hara reservations.

I know there are many huts and some are larger than others. I just don’t want a chance at missing out because i won’t be around a computer day one of reservations. What has been your past experiences?! And any reservation tips?!