So I assume that Expert Flyer shows award seat availability to members of the airlines' own frequent flyer programmes. Airlines commonly release fewer award seats (sometimes far fewer award seats) to other FF programmes.
As an example: Qatar releases award seats to members of its own Privilege Club about 360 days ahead of the flight. It then releases any unsold award inventory to Velocity 330 days ahead (and availability is often still pretty good by then), and to Qantas FF 119 days ahead (forget it).
If you don't have Qatar Privilege Club membership (and/or you don't have Avios to transfer into the programme), your best bet is to be awake at 1am AEDT, 330 days before the flight you want to book, when Qatar releases its flights to Velocity. Availability is often pretty good, but the award flights are usually taken within a few hours. Don't wait until you wake up the next day!
I'm afraid I haven't been following Emirates as closely because I wouldn't pay their extortionately high carrier charges even if I did find availability.