For limited travel options you may consider an alternative solution ot Japan. If you can accept (in osme cases) longer layovers on your way you may book round trip flights from Europe to various cities in Japan already for €347. This deal is based on service of China Eastern Airlines and, in some cases, with longer layover in Shanghai. Since you can get free 72h visa on arrival this is great opportunity to visit this city before you continue to your final destination.. Please look for flights departing from Amsterdam, Madrid, Rome or Frankfurt to Tokyo, Fukuoka, Komatsu, Okinawa or Osaka.
As mentioned travel dates vary by each origin and destination and are very limited in travel period between 19th of September till 8th of December 2016. This is based on date of your outbound flight from Europe to Japan. Max stay 3 months. Below you may find few suggestions from each origin to various destinations in Japan. The easiest way to check your connection possibilities is using Skyscanner.
Booking sample of cheap round trip flights from Europe to Japan from €347! In this case you would be departing from Amsterdam to Hiroshima on 25th of September 2016. Your return flight from Asia back to Netherlands would be on 9th of October 2016.