Yesterday that might have been feasible - today, the Bomford story is in the Australian media and they’d know why they were being asked, and I suspect you’d just get referred to public affairs.
Do you know anyone born in South Australia around 1958-1960?
Their own birth registration should be close in terms of numbering to the Bomford book and page registrations.
For example, if someone born in 1958 was registered in, say, Book 44A, that would support the numbering system in the Bomford certificate.