I’ve now uploaded PDF’s of four ancient Greek calendars to Archive.org. All were edited by Franz Boll, and published in Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Philosophisch-Historische Klasse, vols 1 (1910), 2 (1911), 4 (1913) and 5 (1914). Here are the links:
Franz Boll, who edited them, died in 1924, so these are all well out of copyright everywhere.
The important one for our purposes is the Calendar of Antiochus of Athens. Looking at it, all the entries are astronomical, and concerned with the risings and settings of constellations. I didn’t see any other kind of entry. The notice on 25 December — “Birth of the sun. The light increases” — has no significance, I think, except for the astrological one. It certainly is not a witness to the Dies Natalis Solis Invicti, therefore.