I went without a guide and the queue wasn’t that long. The booking for mountain hut will only open few months before the climbing season (summer). If you have any huts in mind, it would be good to check their website around 3-4 months prior to the climbing season.
I started climbing one day behind you. Unfortunately my shoes started to break on the 7th floor around 3100 meters high, so I couldn't climb to the top. I only go up to the 8.5th floor cottage and walk down.😥😭
