According to Valaran Nara, Thresh and Elise have analogues in Japanese mythology, which is sort of close to Ionia in some ways (I mean, Yasuo is Ionian, he's basically a samurai). I don't think Bloodmoon is restricted to the festival that Shen and Akali put on, more "Bloodmoon" is a description of a certain appearance, typically given to things that are spooky in Ionian culture. Shen has a Blood moon skin because he was playing the part of an evil spirit, Akali has one because she was playing a character who sort of embraces or overcomes that evil spirit by putting on a Bloodmoon mask herself.
From what I understand, Bloodmoon is a larger aspect of Ionian culture, where the festival was just one event that was put on, where Shen and Akali dressed in Bloodmoon style clothes to represent the play they were in. It's kind of like the grim reaper being a symbol for death, and some people putting on a show where one of them dresses as a grim reaper to symbolize someone dying or something.
But these are not canon facts. The only thing which was canon was the JoJ piece with Akali and Shen, in which they enacted the story of Reina fleeing from an evil spirit until the day she resolved to face it, thus making it disappear. But Reina nor her mask was supposed to be about spookiness. In the description of the festival in the JoJ there's no reference as well to this idea.
What's there is:
During the night, Ionian citizens were treated to various musical and theatric performances pertaining to Ionian history or legend.
which could be used to argue the new Blood Moon skin refer to actors playing characters for this performances. But here lies the problem: why are Elise and Thresh Ionian legends? While Kalista is explainable due to her global scope metropolitan legend and Thresh is kind of explainable (not completely, because if he wanders everywhere his deeds in Ionia shouldn't be so many or so frequent to have him become a full fledged mythological creature) because his short lore now says he wanders Runeterra, it doesn't make sense for Elise to be a legend. That would rather hinder her job of deceiving people into following her so that she can offer them to Vilemaw...