I once won a bag for a really good price. The seller already quoted $26 for priority flat rate envelope. When the auction is over, he said he misquoted the shipping cost (the envelope didn't fit, etc) and gave me 2 options; I could mutually cancel the transaction (which I didn't want cause the bag was pretty rare and I got it for a really good price) or I could pay the difference.
Initially he asked for additional $18! I kinda got the feeling he wanted more money because the sold price was rather low and though maybe by asking more money I'd duck out - heck no
In the end, he asked for additional $11 for priority mail with a soft envelope. (it fits after all, with much more space)
With that shipping cost -- $37, I could have gotten an Express mail instead of Priority. It's wasn't even a big bag!
I was annoyed at first, but I wanted the bag and it was still a pretty good deal.
I've sold once on ebay and I had to cover $30 from my pocket. (damn Indonesian PO) I didn't ask for more money to the buyer.
I think you should tell her that it's not allowed by ebay and tell her you're going to report to ebay if she keeps sending you the invoice.
Keep us updated
Good luck!