I've backed big single screw like tugs and ships. When backing, current, wind, prop will always put you to one side. The rudder is usually near useless. Since it is, I put the rudder over in the direction the stern is going anyway and depending on speed, go ahead every so often. Just enough to push the stern a little in the opposite direction, go astern and wait until it's time to go ahead again.
I've backed down narrow channels and around bends this way, many times.
If you back into the same dock, same current with the same effect all the time, make a drag to run on the side you're turning away from. With a little experimenting you can get the backing reasonably straight.