User blog comment:Shaldemar/Prototype: Timeline (Light Novel Vol. 4 until Vol. 9)/@comment-27033694-20161017151855/@comment-27011036-20161018153120

I wrote the blogpost "New World Calendar" to venture into the whole calendar problem. The current state is a little bit behind as is (at the moment) uses information until Vol.9. I'm about to expand this blogpost and in time also the "New World Calendar" post.

One thing that intrigued me in the past more and more is the thinking that Maruyama-sama maybe just used the earthly calendar for easiness. So it might be August = 8th Month = Middle Fire Month and September = 9th Month = Lower Fire Month. But like you pointed out, the whole month vs season thing is a little bit mismatched (believing, Fire = Summer). We have to hope for more details in further (Vol.12 and after) novels.