Cleaning Challenge: Grout

Dear Reader,
How would you clean this absolutely atrocious looking grout?

I have tried baking soda, dish soap, vinegar, borax, barkeeper's friend, magic erasers, tea tree oil (TTO is supposed to be a natural mold inhibitor). . .and various combinations thereof. . .
Last, I tried scrubbing it with a paste of baking soda and hydrogen peroxide because I had read somewhere that it worked wonders. . .Still no effect.

I'm at the end of my rope. Nothing works.

Well, bleach works. But I got rid of all my bleach because it's nasty and corrosive and I want to find less caustic ways to clean things.

Someday, if I have a ton of free time on my hand, I might ask my landlord if I can re-grout it myself. (That's probably the only way it's going to get done this decade....)

Do you have any miracle cleaners for moldy and/or stained grout?

Comment with your solution!