I am planning to do this walk next month.
I'd heard conflicting reports about the conditions on the tops so I contacted friends in Japan who own a hiking shop in Yamanashi (Elk). They also run guided trips most weekends so know the current conditions throughout the Japanese Alps.
Their advice was that there was more snow around this year than there usually would be at this time of year. (Given the very warm winter that is kind of surprising – there must have been lots of snow in Spring.)
They recommended carrying light crampons with at least 6 points, with the caveat that you might not need to use them. Since I have a very light pair of 12 point Salewa crampons that's what I'll be taking, along with my BD Raven.
It'll be interesting to see how the current mega typhoon affects conditions – if it's warm (a typhoon's rain can be surprisingly warm) then the snow will simply be washed away – but if the temperature drops then you'll get metres of new snow, followed by very warm weather (the Foehn effect) meaning a very heavy and unstable snowpack. I'll be playing it by ear.