So was Qurinius govenor 6 C.E. or 4 B.C.? Because most histroians agree Qirinius was governor not at the of Herod the Great.
Also, even if the census could be dated 4 B.C., Romans censuses did not require one to return to their ancestral home. Typically the Romans would just go from house to house where people lived. If returning to ancestral home had happened, surely it would have been mentioned by Josephus right since it would've been a huge event. Thousands of people would be immigrating all around.
Most scholars and historians think Luke was simply mistaken because he was trying to have Jesus fulfill prophecy. In reality Jesus was most likely born in or nearby Nazareth.