Hello,
There's a fine image on the AWM website of an officer wearing the unit and battalion number on his lapels, as you describe:
https://www.awm.gov.au/collection/P03302.001
It was also on the AWM site that I saw the small curved "AUSTRALIA" being worn on the collar of an officer, below the General Service badges - I will do some searching on there.
I have attached images of several instances of the P.M.F. Engineers wearing their badges while serving in the A.I.F.
All interesting stuff, indeed...
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