While Govindarajar had expounded on Shri Ramayana based on the tradition of Srivaishnavam, has anyone elucidated on Mahabharata and Shrimad Bhagavatam?

Yes, there are commentaries for Bhagavatam and Mahabharata as per Sri Vaishnava tradition. There is an elucidation called Sriveeraraghaviyam for Shrimad Bhagavatam and there is also another elucidation called Sukapakshiiyam for our references.