1. You may need an attorney for this tough job.
2. The cover letter has to convince them you are absolutely outstanding in your research area in the international level. You published articles in top journals in your field. You are reviewer for leading journals. Your paper was cited by researcher in top organization. ...
3. Try to find a couple of managers in R&D of a very big company to provide you a strong recommendation, in which your research achievement can be applied in that company.
4. Try to find professors who has high reputation and very strong background in your research field to support strongly.
Any other evidence to support you have international repution (paper published in international journal, attended internation conferences) can be helpful.
I believe a good attorney can help you at this hard time.