The problem is you have no way of knowing how she has been storing the cake so if it is dry it is most likely not your fault. Plus you already know she's a PITA since she haggled with your price.
I would not even meet with her. It is definitely going to lead to an argument and frankly people are a little crazy these days. Who knows what she might try to do. I would email her and tell her that upon further consideration you feel the two of you are not going to come to an agreement about the cake. I would reiterate your policy again - quote her the invoice. Tell her since you do not have proof that the cake has been stored properly since it left your possession and that 2 other cakes of the exact same recipe plus the scraps you tasted were moist and perfectly fine you are unable to offer her a refund.
If you do decide to meet with her take someone with you. A husband or boyfriend if you have it. I know that may seem ***ist but sometimes a man is able to able to keep the situation in check. It's more their nature to not take it personally and keep it business like. Not saying you can't do that, just my experience.
Good luck. Let us know what happens!