Take the $3000 first. Then send her a letter, that you will report to the city of her basement building. She will lose more later than paying you now instead.
Evidence of she knew your no-license status --- She went ahead without permits.
Insist that she hired you as a common labor, not a trade. She told you that she would hire other trades to check you work and she will care about the permit things, though you have never seen any trade on site.
You probme is the $6000. You have no contract. if she say the original oral contract is $3000?