First of all, Rent is a flawed piece to begin with. It exists in a time warp. What was supposed to be happening "now" in the East Village had already happened and the gentrification had already begun. It was outdated before the first performance.
I really can't think of anything that would make rent "edgier" unless they performed it in a place where the audience had to sit with real junkies and homeless people.
I saw the original cast perform the show. Over time, the show has lost its punch. Since 9-11 and the Iraq War, it's hard to find empathy (sympathy?) for the characters in the show.
If anyone ever tells you that you put too much Parmesan cheese on your pasta, stop talking to them. You don't need that kind of negativity in your life.