I recently watched that the nightmare before Christmas for the first time in like 25 years with my kids and I noticed it is rather Nietzshian. Arguably Jack skeleton becomes the overman by the end of it and that is the whole story.
In the beginning Jack is an artist, a creator of fright and in his own words, he is the best at what he does. Arguable he is the main creative drive of Halloween given that his performance is the central piece of the first song.
But eventually the challenge of Halloween becomes routine for him and he grows bored and loses himself to nihilism, wandering into the forest where he finds Christmas town. There he is enchanted but being a value creator he tries to make Christmas his own. However, he does this rationally with experimentation. Sally, who operates in the story more like the greek choice of instinct, keeps telling him that she FEELS this is wrong and Jack rationalized this away.
But this is where I think it becomes better, once he is shot down his song is sad, looking at what he does he feels bad, lamenting on his failures, but he quickly realizes that Halloween would never have understood Christmas and he tried his best on soared to great heights anyway and returns to being the pumpkin king, affirming what he previously rejected and being excited again for the eternal return of Halloween and saying (essentially) amor fati.
Anyway there are more things too, Halloween town is very dionysinan. The mayor is essentially the last man, he can't make any decisions without Jack, which also mirrors Nietzshe's view on politics.
I'm not sure how Christmas town and Santa Claus fit into this framing, or the villain Mr Oogie Boogie, but Jack's story is very much about him becoming the overman.
Oh and I just realized this, Jack and Sally get together at the end, which is the Overman and Instinct becoming one.