I am an Australian with my wife flying into Shanghai from Australia on August 24th this year.

We are also flying directly to SH from Sydney in August and having three nights at a hotel in SH before cruising back to Sydney. My understanding is we do qualify for the 144 hour visa because our flight out of Sydney is direct and our first port of call is out of China - it is Busan. I understand that there should be no stopovers on the flight and the first port of call out of SH must not be in mainland China. Perhaps someone can tell me if my understanding is correct.

That is correct.