It's important to post in the local newspaper. It doesn't have to be where she is, but according to most abandonment laws, this is still considered the best way to reach someone. Use her full name and describe the goats by breed only. This is a must, if you want to be completely legal.
Theory is: someone who knows her might see it and tell her. Most states still have laws written this way.
I agree she's taking you for a ride because she's desperate. You have incurred debt (at least in favor, if not in cost) for vet care for the one that passed, you have fed them significantly longer than agreed, and you have not had use of the space they occupy in this duration that has surpassed the original agreement. Furthermore, your time is worth something. You have had to pursue her, care for the goats, clean up after the goats, and more. She has therefore incurred debts to you for the keep of the goats, and you need to have a ready itemized invoice for this- if not to show her or the authorities, just to show yourself the value of your services.
Go through her facebook page to see where she is. Get someone else to friend her to find out for you.
Post in the newspaper, make your invoice, send her the notice if you can find her, and enjoy your new goats!