I had the exact same problem but I was backing out sometimes single handed and sometimes half handed. Half handed is defined by me to be when I am accompanied by someone who cannot help at all and will probably get in the way or start screaming at the wrong moment. I am an expert in half handed sailing.
Maybe I am too careful--but for the longest time I tied one
line to the starboard stern
cleat (running the
line behind the stern and then looped around the dock
cleat by the port stern), and another to the bow, pushed the boat out of the slip while standing on the dock, and turned the boat around so that it was then oriented with the stern towards the dock. Then I pulled the boat into the slip stern first. Then its easy to leave.
Later one I used the method lancelott describes. Again, single handed or sometimes half handed. Never had a problem.