Hakone Private Onsen Ryokans

Looking to book a private Onsen Ryokan for late May (5/23-5/25) for my honeymoon next year. I feel like I am behind on booking I see some ryokans show May having no vacancies right now, is that because those dates have not been release for booking yet? Please provide recommendations, looking for a Japanese style room, private onsen, kaiseki in the room as well for around $600-700/per night for 2 people.

by doc_gnu