Although the origins of the text matter for presentation, my only thought when reading this text was "man, I wish my flavor of European culture had this as well and I wish it were taught in school at some point".
It may not have exactly this, but it probably has more than you realize. The rush of the 20th and 21st century has crowded out a lot of stuff. The western world has a rich poetry and literature tradition. Given how severed we are from all of it nowadays you may well find you still get that foreign culture frisson from digging into it.
The Japanese version looks quite a bit more grounded in naturalism than the Chinese version, or at least TFA's translation does (i.e. August 28–September 1 天地始粛 vs 天地始肅 [1]). "Heat starts to die down" is not exactly precise but better than "Heaven and Earth begin to Withdraw" and "Cotton flowers bloom" is definitely a lot better than "Eagles worship the Birds".
I'm not the GP but I definitely want a calendar made up of details like this, regardless of it's literary quality.
Chinese and Japanese's version are the same (in this case). Just different translation.
Actually, neither "Heat starts to die down" nor "Heaven and Earth begin to Withdraw" is a good interpretation of 天地始肅.
"Heaven and Earth begin to Withdraw" is a very literal translation. In this case, 天地 = everything = everthing growing from the ground, so 天地始肅 means plants are no longer sprouting.
"Heat starts to die down" is not a translation. Just a convenient English paraphrase.