I did the wikis for January, February, March, April and so on, and then I came across post #71134. Is the Japanese way of writing the month of October acceptable for using the October tag in this and similar images?
Yes, all the months are the number of the month (either in Kanji or Arabic numerals) + the character for moon/month 月, and are pronounced as the Japanese number + がつ (gatsu). There are traditional names too, but those aren't really used in the modern language.