Darin McQuoid Photography
also has some write-ups from a region a bit further north (near Sendai) though he lacks specifics for how to get around.
There is also a region further south in Gifu that runs off of rain that is apparently really nice. As well as the island of Hokkaido which Ben and Rafa explored a bit a year or so ago... but I couldn't find any information from them about what rivers or where they ran.
If you want to go to the Gifu areas or the Minikami area... Yoshiro (Yoshi) Takahashi is the man to talk to (hit him up on facebook). He runs a rafting company and is a class V boater as well. He can put together commercial trips too as a kayak guide if you are so inclined.
For the stuff we did in Minikami (near Nikko), we were there the last week of May and first week of June and had the end of the snow melt. The Kiotsugawa is one of my favorite rivers in the world. Amazing!
The previous year Darin was there 2 weeks earlier and had high water. Both were above average snow packs though. Further north is a smidge later. Not sure when Gifu runs. Hokkaido is probably into July if I recall.