Dear Harry,

Chapter 4 (titled, "Krishna, the Gita, and the Indian Nation," pp. 115-153) of Richard H. Davis's The Bhagavad Gita: A Biography (Princeton U Press, 2015), certainly provides insight into the text's spread throughout India in the modern period. Jnanadeva's work in Marathi, Jnaneshwari was the first vernacular reworking of the text in the "medieval" period, I think, so perhaps looking into some of the scholarship on that might be helpful.

Brad Clough