After a long time, both Shiina Ringo and Tokyo Jihen have official YouTube channels, through Vevo. Most of the videos are uploaded there, with 240p to 360p maximum resolutions. Some of the old ones are 480p, but, in the case of "STEM", the aspect ratio is incorrect: 4:3 instead of 16:9.
Not great, but not bad either, since we can finally share most of them legaly and without worrying about their eventual take-down.
However, it isn't a perfect solution, since some of the videos are locked outside of Japan. Kind of lame, if you ask me.