I have found Star Alliance award availability in long-haul business to be very good. Last year I had to change a flight twice very close to departure and got new bookings with no trouble each time. I even changed airlines, no problem. All by calling the Eurobonus line.

As long as you are flexible with airline and somewhat flexible with departure and changeover details, there should be something available.

In fact, today I just booked a one-way business class *A award from Sweden to Tokyo with Eurobonus points, with departure one month from today. I got exactly the flight I wanted. A very nice person at Eurobonus helped me and it was done in a matter of minutes.

SAS award availability is another matter though!