In addition to advice, provided by dkerr, you may wish to use the [Awards/JL-OneWorld] Method, as it shows negative Award Availability more explicitly:
Yes, JL is a good source, but note that it only works up until 4 days before departure. So for last minute availability, which CX has a habit of releasing, you need another source. Hence why I was using BA or QF. JL is also showing the one F award seat on the 3rd and 4th but won't show anything for the 27th as closer than 4 days from now.
DAK