You would have been better starting a new thread

Looking for open jaw may be more $. You need to look at where UA/AA/QF/TG fly to. LH is from Germany, so a big diversion. Then plug in the main cities/airports. Add STL last, if at all. EK/EY/QR may be an option.
Oneworld has a circle pacific fare, but may be expensive. https://www.oneworld.com/flights/mul...circle-pacific
Or a task for a living breathing travel agent. But they get low commission on cheap economy fares, so little value in them spending hours for saving $100 for you.

A USA Australia return with a nested Australia Thailand return may be best. Or a USA Thailand return with a nested Thailand Australia return.
BNE has limited flights to/from USA. More likely you may have to go via LAX/SFO to SYD/MEL.
BNE does not have that many long haul flights. https://en.wikipedia.org/wiki/Brisbane_Airport and http://www.bne.com.au/bne-airlines-aviation

Airlines that fly USA/Canada to/from Australia (not from all airports to all airports)
- American Airlines AA (LAX - SYD) [OneWorld Alliance] (AS partner)
- Air Canada AC (YYR – SYD, BNE from Jun 2016) [Star Alliance]
- Air New Zealand NZ (LAX SFO IAH YVR via AKL) [Star Alliance]
- Air Tahiti Nui TN (LAX via Tahiti. Last segments on codeshares) (AA & DL partner)
- Delta DL (LAX – SYD) (VA & AS partner) [Skyteam Alliance]
- Fiji Airways FJ (LAX HNL – BNE SYD BNE via Fiji) (QF, AA & AS partner)
- Hawaiian HA (HNL – SYD BNE) (AA & VA partner)
- Jetstar JQ JQ (HNL – SYD BNE)
- Qantas QF (LAX SFO JFK DFW HNL YVR*– SYD BNE MEL) [OneWorld Alliance] (AS partner) {* seasonal}
- United UA (LAX SFO – SYD MEL) [Star Alliance]
- Virgin Australia VA (LAX – SYD BNE) (DL partner) MEL LAX restarting 4 April 2017
And others via Asia & Middle East

Various airlines fly to Thailand. Is a popular destination for Aussies. Look in google flights as this Example

And Qantas does not have a u