No pagan feast is fixed on December 25th, and the Church chose this day to set aside as a celebration of Christ, so it is not a pagan feast by definition.
You seem to confuse facts with assumptions.
For your review:
Messiahmas? On the Birth Date of Jesus of Nazareth
b'shem Y'shua
(1) Your source concurs that the identification of Succoth as the day of Christ's birth is simply a theory based on a number of suppositions and inferences. Your source makes as good an argument as can be made, but it remains a theory without enough Scriptural data to make it definite.
(2) Your source knows almost nothing about classical Roman antiquity. Not only was the Babylonian calendar different from the Roman calendar - but Constantine and his family were never involved in the Babylonian cult.
His family was Greek with possible Brythonic and/or Dacian ancestry and their paganism was of the traditional Roman sort, perhaps admixed with then-fashionable Persian Mithraism.
I have studied the Bible and theology for a while and I have to say that I learn more serious Biblical truth from Messianic Jews than from any other Christian body.
Sometimes I wish I was a Jew just so I could be a Messianic Jew!
Bless you and keep 'em coming!