I guess every country will be different. Australia is similar to Europe.
It depends on the device but something like this would most likely not require mandatory safety certification and compliance marks but a manufacturer would be responsible to ensure that appropriate Australian standards or other appropriate international standards have been met and would be required to demonstrate this if challenged. The testing that you have conducted seems appropriate due diligence given the assessed risk of proximity to higher voltages and the test reports would be suitable evidence. It is an obligation on the supplier to ensure that products manufactured in future are materially the same as the product tested.
Interestingly the AC and DC plug packs are declared devices and must be tested in a NATA certified lab and have a certification mark applied though there is no need for factory inspections, again the manufacturer/importer needs to ensure that any future product is materially the same as the certified and tested product.
EMC (FCC type requirements) for a device like this would require the manufacturer to identify appropriate Australian standards, test to those standards and self certify compliance by an Australian based business with registration on the ACMA database and have reports and evidence on file to provide to ACMA on request.
You proposal seems reasonable and practical, but Intertek seem to be leveraging the situation to make an unreasonable request. Hopefully they are open to sensible negotiation.