@Amorphose: you could try Yahoo Auction Japan and use a middleman service like Crescent Shop?
A tape like that in japanese is a コンパクトカセット or in short カセット, so if you search for 宇多田ヒカル カセット or something, I figure you'd find something.
Edit: I just searched and on this very moment the Distance tape is on sale, bidding starts at 1000 yen (10$), so if you really want it, hurry up and make a Crescent shop account!
let me know how it went if you decide to try!