The major goal of an away rotation is to audition for a potential match there. An LOR is a very secondary goal. You don't need a LOR if everyone knows you and wants you to come there. So that's really why folks do these away/audition rotations. You are solid at 3 away rotations, you probably get 3 interviews. You just get a LOR from an away rotation, you probably don't add incrementally to what your application would look like if all your LORs came from your home school. Keep your eye on the prize; The real prize is an interview leading to a high match, not a nice letter which really keeps you at ground zero when you have to interview elsewhere. You should be doing away rotations with the goal to lock in an interview with folks who think you come off well in person. Nobody puts great stock in an LOR from an away rotation where they away rotation itself didn't want you.