I think I have solved it. Think I have, anyway.

The two designs are NOT directly referencing Tsukuyomi, but you pointed towards something else. Tsukuyomi is the Shinto god of the moon, which somewhat refers to the "rabbit in the moon" mythology in Buddhist texts, which points towards Konjaku Monogatarishū, the Honchō section of which is where our story is contained that comes from Buddhist Japan in the late Heian period. The Konjaku Monogatarishū, in short, is an anthology on the teachings of Buddhism's journey to Japan.

The story begins with an old man begging for food from the three companions: the rabbit, the monkey, and the fox. The monkey gathered fruits from the trees while the fox wrongfully pilfered a lizard and a pot of milk-curd. The rabbit, who knew only how to gather grass, instead offered its own body, jumping willingly into a fire the man had built. Despite this, the rabbit was not burnt. The old man revealed himself to be Śakra and drew the likeness of the rabbit upon the moon, having been moved by the rabbit's virtue. It is said the image is still draped in the smoke that rose when the rabbit cast itself into the fire.

In addition, Tsukuyomi's traditional offering in Shinto mythology is rice cakes; the same thing the Moon Rabbit makes tirelessly by the Buddhist ideology.

Ash is draped in smoke, dark as the moonlight, and the two guises you present here, Blue and Red, represent the Monkey and Fox, respectively. As for Tsukuyomi, he is the Rabbit of the story (which, coincidentally, would be Lotus as her old home was the moon prior to the Fall of the Orokin).

Am I close?