So what happens if I drive my car into Austria or Italy with just my normal headgear - assume I'd be stopped by the Feds?
A helmet is definitely required and it gets worse than that. Strictly speaking you have to have a motorcycle licence too, ridiculous though that may seem. There would however be some confusion because Italians who had a car licence up to about 15 years ago could ride a bike without having a specific bike licence. You could also probably get away with explainining that you are not required to have a bike licence for this type of vehicle in your home state and that under international agreements you only have to comply with your home state rules for licences to drive a vehicle registered in your home state whilst visiting another EU state.
I am not sure if that is entirely true for road vehicles but you would probably get away with it.
Recently the Swiss police have taken great delight in confiscating bikes of Italian riders who do not have an endorsement for bikes on their licences. The recomendation is that holders of the old paper licences get their licences updated to the new plastic type and request the motorcycle endorsement.