you can do whatever you want but the bottom line is: you're an political asylum holder under the protection of the U.S. due to the prosecution you suffered or would suffer in your native country. if you need some coziness in your life and would like to use your national passport for your convenience or savings they (USCIS) may entertain the same right and comfortable deny your further stay in the U.S. assuming that you have obtained your asylum on a fraudulent bases.
we are so often pissed off withthe Goverment for treating us unfair but if I have been an USCIS officer and have seen your cute little game with two passports (RTD is NOT a passport, btw, you are getting a privilege to have it in lieu of your national passport you're unable to use given your status) I may be a human also and assume that all of them (asyless) are the same - fraud and cheaters and would, without a blink of an eye, deport you back.
political asylum is a serious thing. you are not. good luck with your savings on visas.