The problem with that date is that April would be when an agricultural society, like most of Roman subjects would have been, starts planting their crops. After a long winter, their wealth would be at a low point and there would be very little to collect, which was the reason why Mary and Joseph were going to Bethlehem.
>> “which was the reason why Mary and Joseph were going to Bethlehem” <<
The real reason was because it was the commandment to go to Jerusalem for the Feast of Sukkot. Joseph also was required to vote in a Roman plebecite, from his home village, which was Bethlehem.
The conjunctions of the particular heavenly bodies that the Jewish astronomers from Babylon observed were also verified to have occured then by NASA computation.