AC is simplest option. The cost is only one part of travel.
CX & Kong Kong is a political risk.
SYD BNE is about 1:30hr if you cannot find an acceptable flight into BNE.

Airlines that fly USA/Canada to/from Australia. Following the pandemic, routes are being restabilised and some new routes. Schedules can change. Route restart dates subject to change.

• Air Canada AC YVR – SYD BNE. [Star Alliance] .
  
• Air New Zealand NZ LAX SFO IAH YVR via AKL. [Star Alliance]
  
• Air Tahiti Nui TN LAX – via Tahiti & AKL. Last segments on QF codeshares. (AA & DL partner)
  
• American Airlines AA LAX-SYD due to restart 29 Oct 2022 [OneWorld Alliance]
  
• Delta DL LAX – SYD. [Skyteam Alliance]
  
• Fiji Airways FJ LAX SFO HNL – NAN - BNE SYD MEL ADL. (OneWorld Alliance connect. QF AA & AS partner)
  
• Hawaiian HA HNL – SYD. Pre CV19 also used to fly to BNE (AA & VA partner)
  
• Jetstar JQ HNL – SYD. Pre CV19 also used to fly to/from BNE & MEL.
  
• Qantas QF SYD - LAX DFW HNL YVR*; BNE - LAX ; MEL- LAX. {* seasonal}. MEL-DFW due to start 02 Dec 2022 (new route). SYD – SFO due to restart 30 Oct 2022. SYD-AKL-JFK planned from June 2023. Pre CV19 also had SYD-SFO & SYD-JFK(via LAX). [OneWorld Alliance]
  
• United UA MEL-SFO, SYD-LAX SFO. BNE-SFO from 31 Oct 2022 (new route). MEL-LAX and SYD-IAH due to restart 30 Oct 2022. [Star Alliance]. (VA partner)
  
• and others via Asia & Middle East