I am looking for studies that have looked in depth at the practice of caste system (as we understand it in the Hindu sense) as well as other stratifications (such as Arab lineage versus native convert) among various Islamic communities in India.
There definitely are, and I will look for some of them. The only ones I remember reading are about the continuance of caste practices stigmatizing Dalits following the conversion to Islam. For example in the case of the Valmiki.
Leslie, J.(2003) Authority and Meaning in Indian Religions: Hinduism and the Case of Valmiki. Ashgate publishing.
There is some older work such as: Ahmad, Imtiaz (ed.). 1973. Caste and Social Stratification among Muslims in India. New Delhi: South Asia Books.
Mines, Mattison. ‘Social Stratification among Muslim Tamils in Tamil Nadu, South India,’ Caste and Social Stratification among Muslims in India. Imtiaz Ahmad (ed.). New Delhi: Manohar Publications, 1978.
Goodfried, Douglas. ‘Changing Concepts of Caste and Status among Old Delhi Muslims,’ Modernization and Social Change among Muslims. Imtiaz Ahmad (ed.). New Delhi: Manohar Publications, 1983.
Lindholm, Charles. ‘Caste in Islam and the Problem of Deviant Systems: A Critique of Recent Theory,’ Muslim Communities of South Asia: Culture, Society and Power. T.N. Madan (ed.). New Delhi: Manohar Publications, 1995.
And some more recent work: Ali, Syed. ‘Collective and Elective Ethnicity: Caste among Urban Muslims in India,’ Sociological Forum. Vol. 17(4), December 2002, pp. 593-620.