If you're set on fixing it, you can put 700's on it and get long reach brakes as per sivat. Tektro's work pretty well in my experience although you you may have some joy mounting them or, as Dersu said, your existing brakes may be long enough to reach. For a beater, I wouldn't go out and buy a 27" fixed hub wheel... sort of defeats the purpose of keeping it cheap. You can swap or sell a fixed 700c much more easily if you don't like it or move it to a better bike eventually if you do.

I have one of these I pulled out of the garbage that I'll be fixing for a low speed winter commuter. They work great for that.