My only experience was 2 years ago when I was able to get 2 award tickets in Club World from the US (one ticket originated at LAX and the other DFW) to Mauritius, the Seychelles, and Nairobi. I booked the tickets in mid-May for a mid-June departure and got the exact dates and flights that I requested. I would consider this to be a prime travel season (at least for the transatlantic portion it definitely was) for some fairly "hot" destinations (the normal price for these tickets was about $12,000 each) and yet I had no problem getting exactly what I wanted. I don't know whether this is a typical experience or if I just got lucky.