It looks like things have gotten better in the hour since I left the office. The inbound took off on-time and now my flight is delayed by less than it was.
A couple of people brought up the fare class which is the crux of the issue. My fare class on the LAX-SFO-SYD ticket is G (PZ from SFO-SYD if it makes a difference), and when they are changing my ticket the lowest available appears to be V. So it’s not showing any SDC options.