Are there any travel agents in Japan that offer cheap domestic flights -
fares can be purchased online?

I know ANA's own website is half-way there, but you have to ring to make the
final payment arrangements (real hi-tech).

I am not in Japan now, but want to try and make arrangements for August
(peak season, ie: cannot use Welcome to Japan/Visit Japan discount fares).

The low-cost carriers also refuse to have English website (eg: Skymark and
AIR-DO aka Hokkaido Int'l Air Lines).

Any advice would be appreciated.