Possibly the old-fashioned word mumpsimus would work for you. One1 of its definitions is
1.1 A person who obstinately adheres to old customs or ideas in spite of evidence that they are wrong or unreasonable. (Oxford Dictionaries)
It's not a common word, and it has a bit of a connotation of the stubborn person being old or set in his/her ways, rather than just purely stubborn.
It's ironically appropriate for your example from the classics, as it is from a story about a priest who mixed up the nonsense word mumpsimus for the actual Latin word sumpsimus but refused to change even after being made aware of the mistake. You can read more about the origins in Wikipedia.
Tiresias is after all the only one that can force Creon, a king and a mumpsimus, to see reason
Jade was called a mumpsimus because she continued arguing for three days after she realized her opinion was scientifically wrong.
I think it works very well for your Creon example, since he was old(er) and most Classicists will probably know the term.
It also works somewhat for your second example, since it looks like Jade is sticking to an outdated idea that is factually wrong. However, I would expect a casual audience to be less familiar with the term, and if Jade is a young person the connotations might be a little off. (On the other hand, it sounds kind of insulting all on its own, I think, and if your listeners aren't familiar with the term they can't object to it based on its connotations.)
1 It can also be the idea that is stubbornly retained.