I have Tardive Dyskinesia as a results of various psych drugs, and also some movements associated with Tardive Dystonia.
Since the drugs have really helped your psychiatric symptoms, it is a shame you may have to stop them. However stopping the drugs is the best chance of the TD or TDy resolving completely.
Once established there is no cure (a small percentage remit spontaneously) but there are drugs that can help the symptoms. Clozapine is recommended as it is the least likely antipsychotic to cause or worsen TD. Quetiapine is the next best in this respect. However all these drugs have many health risks associated with them, especially in the long term, that you need to consider.
Often on another Antipsychotic the symptoms are masked and do not reappear until/unless the TD reaches a much worse stage. So if it is felt you need to stay on an antipsychotic drug, that is seen as the best option.
I found this article (you have to pay a small fee to download it):
Tardive movement disorders: a practical approach -- Saifee and Edwards 11 (6): 341 -- Practical Neurology
It gives a good overview of Tardive movement disorders and a treatment map of what to try in which order . There are other things that have been tried, like ginkgo biloba which showed some hope. And B vitamins. You can research these.
It may be worth trying to track down a neurologist/movement disorder specialist with a particular interest in Tardive movement disorders, to get the best advice.
I have schizoaffective disorder and came off psych drugs. But they weren't helping very much and I suffer very badly from side effects. I am very depressed all the time and have psychosis off and on. If there were a drug that would help me and not harm me, I would take it.
Wish you good luck.