I had an identical issue 3-4 weeks back and it's BS, pure and simple. Nothing to do with married segments or phantom availability. There is plenty of MEL - SYD and SYD - MEL availability but one agent I spoke to let slip that they had been instructed to steer people wanting to book MEL - SYD legs as part of OWAs onto the flights with least demand. In other words they have been told not to put you on flights between 7.30 am and 11.00am or prime time afternoon/evening flights.
In my case I was to be arriving in SYD from HND on JL51 at 6.10am and needed to book a connection to MEL. I saw J availability on every flight after 7am but when I told the agent I wanted the 8.30 or 9am flight she said there was no availability before 11.00 (this was about 345 days out). I said I was sure there was availability earlier and I didn't want a 5hr transit in SYD after a 35hr trip home from Europe. She then admitted she knew there actually was availability which she wasn't supposed to book for OWAs. In view of my 35 hr trip she said she would need to check with a supervisor. She came back a minute later and said I could have my pick of whatever flight I wanted.
The reality is that QF want to hoard those J dom seats for their business customers.

This is what appears to happen to me. I need a flight arriving that departs MEL after 7PM (schedule arrival needs to be after 8:10PM to maintain less than 24 hours in SYD) on a Sunday and they said there is "no availability" for 7PM onwards and I had to book something earlier in the day. I just received a call back after 3 hours then the agent who answered hung up on me. So I've had enough waiting for the phone today and will attempt again tomorrow and be more assertive with my booking request. Thanks heaps for the insight!
So after HUACA finally got through to someone today as wait times are lower, pretty sure they were in Manilla?
What I need is currently I'm booked SYD > YVR 7th March 2022 in J as the first leg on my OWA. I want a flight 6th March 2022 with 19:00 or later departure (to have a less than 24 hour transit in Sydney).
The agent said there is 0 availability on any flight in any class (even with cash) departing 19:00 > 18:00 7th of March, which conveniently is the exact times I need to transfer in Sydney.
After HUACA I finally got Auckland which was significantly more helpful, they actually explained what was going on which is what I started to suspect. Because its the first flight of my itinerary its ticketed as a long haul SYD > YVR, I'd be changing the ticket to MEL > YVR with a transit in SYD which isn't available. They said the only way I could possibly fix it is cancel the whole booking and do it again. Obviously that isn't a risk I want to take for 1 short flight.
TLDR computer says no, I trust Auckland to be telling me the truth and I'll just have to book my own flight. Sucks that the computer plays these games but I can live with it.