Wow thank you for all that work Nate! A table like that showing the dates each year into the future is definitely something we need to add to a resource list somewhere.
So the column labeled Hekatombaion 1 is the first day of the Greek New Year, and Gamelion 20 is what we believe is the actual birthday, or the 20th closest to his actual birthday? Maybe it would be a good idea to somehow annotate those column headings in case perhaps someone cuts and pastes the table and it gets separated from the text.