You can do whatever you want. There is no law, just yet, that precludes you from renewing your national passport, especially if your national passport is of a country different from that from which the asylum was granted to the principle. I am not saying yours is, I am just pointing out another nuance. You can have a long conversation about that not being a good policy, I am referring to renewing the national passport, but it will do no harm to you if you renew your national passport or travel on it.
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: firstname.lastname@example.org; Phone: (866) 456-8654; Fax: 212-964-0440; Cell: 212-202-0325. The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.
It is never wise to renew a passport from a country of which you and your family fled.
I suggest that you get a RTD and learn how to be patient for 2 more years.
You are super lucky to be in the US ... don't push your luck.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.