Other half was an elder and only knows of 1 instance where an appeal worked and that involved a legal issue.
I think your first concern should be with your parents. If they refuse to accept that you are adult enough to make your own decisions about your beliefs but still think you are old enough to be their main care providers then there are some issues that you need to talk through.
I am afraid that parents can be far to controlling and, whether deliberate or not, very manipulative. Maybe I am doing you and your parents a great injustice with these thoughts, if so I apologise.
Assure your parents that your love and concern for them hasnt changed and hopefully this will help to overcome the barrier imposed by the JW's.
If not you might have to consider approaching social services and requesting care for your parents. You would of course have to tell them why you are no longer allowed to provide this yourself. This would not be a good witness for the local cong, and the elders might be willing to talk to your parents and reach a wokable solution to avoid such bad publicity.