If you don't want them in there next to your food (and I don't see why it would really matter, they're usually vacuum-sealed in their own bags and the steaks are in their own packaging so there wouldn't be any cross-contamination) you could always get a small freezer just for rats/mice. I might have to go this route for my BP as my mom also hates the idea of rodents in the freezer.
Maybe you should try and get a pet rat. Take care of it, handle it, help your phobia of them go away. Sometimes knowledge of an animal is enough to erase (or at least diminish) the phobia of that animal.