I've had a problem backing out of a slip as the bow "walks" to Port. I have virtually no control over this with the rudder. I finally solved the problem by using a line fixed to the length of the dock and block that runs along it. A second line is fastened to the block shackle and runs through the bow hawsepipe to the cockpit.I keep that line taught as the boat backs out which keeps the bow sliding parallel to the dock, then let go as the bow passes the end of the dock. The line slides through the hawsepipe and remains at the dock. My question is whether this side "walk" is common to all of our boats. Perhaps it is a characteristic of the particular propeller I am using. It remains a problem when I have to back up into the slip for haul out by a travel lift.
I've found finesse to be useful in backing. I started out using a lots of power thinking more is better and realized very quickly that sailboat hulls aren't really designed with propellers in mind. The technique I use for backing now is to apply a little power to start just to get the hull moving slowly and then put the engine in neutral to coast. Now that you have a little water flow past the rudder, you can straighten out from the sideways thrust of the prop, then apply a little more power, and back in neutral, coast and straighten. Eventually, you can apply a lot of power. It is all about the flow of water past the rudder, in reverse you can't fight the prop wash.
Your solution using warps is good and practical, pulling is good, pushing, like with a boat hook, just doesn't look so good ;-)