CA
“The Gemara in Rosh Hashanah says that Tishrei is Rosh Hashanah for non Jewish kings so when referring to a non Jewish king reign it would be the 11th month”
Your post was written fine. I understand you completely.
However the Gemara (almost explicitly) states not like that.
In the tzad that Daryavesh is considered like non-Jewish kings The Gemara quotes passuk reffering to Tishrei as “chodesh hashvii” and asks why it isnt a new year. The Gemara doesnt even address, and takes it for granted that even if it is a new year, and is the first month of the new year it is still “chodes hashvii”