I am getting (LAX-SYD) Y only on 26/12 and Y and J on 27/12. When I click on "Next Day" on 27/12, it comes up again on 27/12. I am guessing that this is 355 days ahead, and won't go any further.

Why not sign up for (free) membership of QFF? This will then let you go in and have a look at these flights yourself (you do not need to have the appropriate number of points to look, only to hold seats).

Dave