Pardon my ignorance if I'm misinterpreting things, but to a casual observer Harukotan seems to be strongly inspired by Far Eastern architecture and cultural motifs.

To that end, are the different forms the daybreaker and nightfaller natives come in actually recognizable as being inspired by specific mythological beings (Yokai, oni, kami etc), or are they just a random mishmash of forms that just happen to have a vaguely reminiscent nature?

No, you're right. Everything about Harukotan is distinctly Far Eastern, more specifically Japanese, in aesthetic. The image of the planet itself is resembles a taijitu (aka yin-yang).

They are probably inspired by oni. Especially the Red Oni, Blue Oni story.

http://montages.blogspot.com/2006/04/naita-aka-oni.html