Beware of people suggesting you use agents. It basically means you will pay a bribe to bypass a requirement. Once you start this method there's no way to get off it.
The problem is the Australian embassy in Bangkok will not provide the affidavit required by Thai immigration, so you are confined to the
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baht monthly transfers. I simply used the OA visa to get free entry into Thailand, and then commenced the transfers. As soon as you have 12 monthly transfers under your belt, leave Thailand and re-enter on the O visa
There is another option. If health insurance is declined, the applicant can use the value of assets in Australia (bank accounts, shares, property etc) in lieu of insurance, provided it's to the same value.