You should go well before your due date. At least a week or more, to be on the safe side. Leaving it until the last minute is asking for trouble, if there any issues with your documents.
If you apply for an OA Multiple entry visa, you can show AUD 54,545 in an Australian account (which is a lot more than 800K THB). For a NON O (retirement) visa obtained in Oz, you need to show AUD 2000. If you will obtain a Non O visa based on being over 50, in Thailand and then a 1 year extension of stay, you will need to transfer 800k into a Thai bank account.
It also does seem to make a difference if there is time spent out of the country in between tourist visas or visa exemptions. Visa runs, as you mentioned, where you jump a border, get a visa, and come straight back, or a border run with an exemption, is a good way to attract the wrong kind of attention.