If you need to plan in advance...
As a gold, you should be able to book confirmed seats in Y as a benefit (additional availability).
Then, keep checking for J availability up until T-24 - if it comes up, great, if not, you have to slum it in Y.
You can cancel the Y redemption without penalty.
Now, you'll be saying , "but I don't have enough Avios to do that", but in the past, I've done this. You take a risk when on the phone because you have to cancel the Y tickets and get the miles back before the J seats disappear, but it is do-able if the agent knows what they're doing and wants to be helpful (BAEC CS reps get a bad rep on here, and I agree there are some who don't seem to know the meaning of either of the words "customer" or "service", but on the whole, most of them are very good).
I've seen availability (not necc. to SYD) start to increase from around 6 weeks out, up until the day of the flight. You need to keep an eye on it, though, as many people booked in WT+ will be watching for an UUA opportunity.
(I don't know of any reason for it to be especially busy then - Lions tour finishes around 7th July IIRC).
Good luck. Keep checking.