AFAIK, if the county your car is registered in requires the more advanced smog test then you must pass that type of certification.
On the oil overfill… I doubt it has anything to do with it. I’d be more inclined to look at the O2 sensors and, hopefully not, the cats.
Maybe clean the MAF, new air filter, new plugs, anything you can do to make it run as efficiently as possible. Does it have an oil separator like the E46 does? If so, and it’s tired/failing, it could be sending much more oil to the intake than normal. Perhaps that has something to do with it too.