Look at an non o-a in the Sydney consulate website. If you have a regular GP the medical certificate is easy. If you have no criminal history so is the police report. Then you need to show money in Australia only. I think your wife can get a trailing spouse non-o on the o-a. Then you are stamped in for a year. Yes you'll need insurance but can use Australian travel insurance now that you probably would have bought anyway.
Go to immigration and request an extension that they will deny but still give you a 7 day extension to leave Thailand. 1900 baht but no overstay repercussions.
If you come visa exempt you'll be stamped in for 30 days extendable at immigration in Thailand for another 30 days. If your O-A is approved and you leave and re-enter you would be stamped in for a year. But you need to enter to get the new stamp