Firstly, yes, an emergency Aussie passport can only be used to fly home to Australia. But you have lots of time. You can go online (find the “real” Aussie website in Bangkok), and apply for a new normal passport. You fill in an online application form, then follow the bouncing ball. I am an Aussie living abroad (Hong Kong), and my new passports take about two weeks from start to finish. Good luck.
Also in the interests of clarity, if you stay for “two full months” (without an extension) you will overstay. Your visa exemption period is 60 days (59 nights). People have reported getting caught out by this before. Good luck.
I realise it’s too late for this application, and you’ll have to reapply, but in certain fonts there’s two common traps, O (Oscar) / 0 (zero), and upper case I (India) / lower case l (lima). I work around this by using copy-paste from a reliable original text. I say reliable TEXT because copy-paste from an image (such as a Passport scan) can transpose these similar looking characters. Good luck.
Was each visit two to three weeks, or two to three months? To an Immigration Officer, the former makes you look like a happy tourist, however the latter looks like a visa dodger.