There isn't really a single noun for this. Most words relating to women who might typically wear a lot of make-up don't really focus on their make-up.
The word 'tart' as a noun really means 'prostitute', when applied to women. However you can use the term more neutrally, as in 'The restaurant was tarted up to make it look like a palace". If you said 'I want to get tarted up for the party', it doesn't meaning that you want to be a prostitute, but rather that you will wear sexy clothing, apply makeup, perfume, etc.
Therefore if you say 'tarty makeup', then that's modifying makeup, and it's not to say that the person is a tart (i.e. a prostitute), but that the makeup is 'excessive'.
'Gaudy woman' is absolutely fine. You can also refer to 'slap', which is a slang and mildly derogatory term for make-up, e.g., 'a woman with too much slap'.