@buzz, the Celestron and SkyWatcher mounts already handle backlash in this way, by doing an initial fast slew to a position that's offset from the target by the same amount every time and then doing a slow slew to the target that's always in the same direction.
I think the error in Ra comes from not allowing for the time this slow slew takes - 3 to 4 seconds, which is about the same as the error.
Chris