Although the Braisa in today's daf implies that the levi'im say the shir of rosh chodesh and not shabbos, the gemara explains in the name of r' safra that it just means that the shir of rosh chodesh comes before the shir for shabbos. On that the gemara asks, we should say the tadir comes first - so shabbos should be first. Tosafos comments that the question of Tadir can be asked even without r' safra. Clearly, Tosafos implies that Tadir is not simply a sevara for kadima but even it is even a sevara to choose the shir of shabbos rather than rosh chodesh. See Magen Avrohom 684:2 who points this out. Tosafos here is lishitasam in Tosafos in Yoma 33a (ein ma'avirin) where Tosafos claims that ein ma'avirin al hamitzvos is a sevara of kadima, but if you have to choose one or the other you use the sevara of tadir.
Also, if tadir is a sevara deoraysa, how can we override the sevara of tadir in order to publicize that it is rosh chodesh?