Thyagaraja Swami was indeed a devotee of Srirama. In this caraNam do not interpret that he is asking moksham from Shiva; the divine name ‘Shiva’ that occurs in the caraNam “vInA gAna lIluDau shivamanO” is to be understood refers to Sriman Narayanan. Even in Srivishnu Sahasranam, one of the divine names is ‘shiva:’. That is, it means One who grants auspiciousness. Moreover, since he bore the Sripada tirtham of Emperuman on his head, the name Bhiksadana changed to Shiva, which is a common, suggestive name.
Since the divine name ‘shiva:’ is found in Srivishnu Sahasranam, we can understand that this name refers to Srirama only.