Just a little bit of background for those who aren't familiar with the .jp cctld.
Once upon a time, there was only .co.jp available as the main cctld for companies in Japan. Emphasis on companies, as you had to show your company registration documents to obtain a .co.jp and organisations were limited to one domain each. At the beginning, that applied even to companies as large as Sony, Toyota etc. The extension was slightly loosened, but remains relatively tightly restricted today.
Later, .jp was introduced as a much more liberal extension. Basically, apart from some reserved words (major geos of cities and prefectures, government offices etc.) anyone could register anything in .jp, and that's still the case today. There are no restrictions on the number of .jp domains that one entity can own, and you don't have to be in Japan to do so, though you do have to have a local contact as the Admin address.
.jp domains are pretty expensive if you're only able to operate in English, as that's a very niche market and there are only a few firms serving it. In Japanese, the prices come right down as hundreds of companies are competing in the space.
It is possible to register .jp domains in IDN (i.e. in Japanese) as well as in ASCII characters.
For English-language .jp registrations, your best bet is probably
http://www.jp-domains.com/ as they have an English language interface and also can help with the local address for the admin contact.
On the drop front, there used to be a (relatively private) English language drop-catcher, but they seem to have left the business and now there are only Japanese firms competing in the drop space. As far as I am aware, none publish "drop lists" so you'd have to compile your own if that's something you're interested in.