Assuming that the only change was swapping the engines.
I think that you should tread carefully - as in contact VicRoads directly. A VX Ecotec is
similar but not
identical to a VS Ecotec and they are required to meet different emissions laws. Deleting the VX EGR and using VS Series II engine management (presumably) means that the VX no longer complies with the relevant ADR anyway. You may, however, be able to argue that it is the same as a Series III VS, mechanically at least.
Replacement engine is identical to the original engine
It is not.
or is an option allowed by the manufacturer for the same model vehicle. The optional engine must be offered in Australia by the vehicle manufacturer as an option for that vehicle (or certified variants).
As installed, it is not.
The change of engine may be recorded by VicRoads provided that the registered operator or a motor mechanic, or dealer in that make of vehicle or an Automotive Engineer signs a declaration certifying the engine is optional for the vehicle model and that all modifications made by the manufacturer for the same vehicle model with that optional engine have been completed.
If you were converting (say) from a VS V6 to VS V8, or using a V6 engine from a VS Statesman or ute (a certified variant) in a VS Commodore, meeting the same ADR's or later, then you could, as the registered operator, sign the declaration that the engine, engine management, brakes etc. are the same as a factory option for your vehicle.
You then take the responsibility for that to be so.
If you are prepared to sign the dec. that the VX engine is identical to the VS engine (again, it is not, although perhaps to a Series III V6 it is close, except for engine management) they might not check too far. To be fair, in practice it will make little difference in terms of safety or emissions; using the VX engine in a VS meets the intent of the law, just not the letter. There is the
potential for an insurance company to refuse a claim or similar though. This is also true if you are driving a vehicle (like now) where the engine number doesn't match what is recorded for it.