Certainly one may rely on a psak from Reb Moshe.
Reb Moshe's basis is that the Magen Avraham quotes a Bach that one may not wear a talis at night. Even though he acknowledges that this may be specific to a talis and not apply to tzitzis, there is a possibility of issur involved. Even though according to Tosafos and the Rosh there is a mitzva to wear tzitzis at night on a garment usually worn during the day, Reb Moshe writes that one would definitely never be punished for not going out of the way to wear a four cornered garment at night. He concludes, as you wrote, that there is no need or hiddur to put the tzitzis back on. However, it seems to me that since we do follow the opinion of Tosafos and the Rosh, that one who putts the tzitzis back on at night would be fulfilling a mitzva, and it should be at least a hiddur. I found that both Piskei Teshuvos and R' Tzvi Cohen in "Tzitzis Halachos Pesukos" agree with my reasoning.
Therefore, I still feel it is preferable to put on the tzitzis, but one would be completely reasonable following Reb Moshe who does not recommend it.