In theory that could work. In practice it probably won’t. Many offices will say that you need to leave and come back on a “clean” stamp to get the Non O and subsequent extensions.
The limit of two visa exempt entries is if you enter via a land or sea border. There is no technical limit on entries by air. That said you won’t get away forever doing them. At some point an immigration officer will pull you aside or just deny you entry.
On each exempt entry you can extend once for a further 30 days at a local immigration office for 1,900 baht.
Why would that matter? They’re not applying in Bangkok so they can get one on any visa status, as long as they have a TM30 filed. Whether that’s from an hotel, an Airbnb or a long term rental contract makes not difference.
I have no idea why your baggage wouldn’t be checked through to your destination because usually using a transit airport they would be.
If your purchased two separate tickets Brisbane to HCMC and another onto Bangkok then that would explain it, but on one ticket it should be checked through.
If you are certain it won’t be then you may have a bigger issue in that you will indeed need to pass Vietnam immigration to collect the bags - which means you would need a visa. Assuming you have an Australian passport, Australia is not on the list of visa exempt countries. Your airline almost certainly will not let you board the plane if you don’t have a correct visa.
The dates on the form are pretty much irrelevant. I have no idea why they are even on the form. Some offices will allow you just to write “Multiple“ and leave them blank. Others will insist on you filling out some dates - even if they are just “guesstimates”.
How is anyone supposed to know on a year long multiple entry permit what dates they may be leaving and returning on say 9 months down the road.
I think you’ll find the airports may only sell single re-entry permits. I may be wrong but I’ve definitely read comments saying as such. Might be a specific officer or specific airport though.