Personally I think £550 sounds like a fairly good deal, especially for a direct flight - I'm not sure you'll find JAL or ANA offering anything much better!

Alternatives would be to look at flights on AY via HEL, starting from KIX or NGO. Both are easily accessible from Tokyo with a short (and often cheap) domestic flight/a short and less cheap train ride.

If your daughter is happy to do so, I'd say there's potential for the Asian version of an ex-EU if you depart from ICN. In my experience Seoul often has significantly cheaper flights than Tokyo.