Why don't you ask (read: bribe with money) your friends in your program to write the letters? They probably know different aspects of your research and could highlight that as well as any professor could. As well, it would probably be less difficult for them; it's always easy to write about someone else.

I would never be able to write three reference letters about myself, because they would be too identical. I wouldn't know different things to highlight, and they would all bave the same style.