What about Mehta and Seshadri (Math. Ann. 248, 1980)?
Their paper handles the genus 2 or more cases (with a focus on one marked point), but my understanding is that their result and proof (generically) generalizes to genus 1 and 0 (and arbitrary many marked points). Perhaps a good project for your student would be to read their paper, and explain how the genus 1 case can be deduced from their work.
However, I recall reading in a different paper that a detailed account of the genus 1 and 0 cases is in Seshadri (Asterisque, 96,1982); but I have not seen that myself.