Someone out their must have a full/cutaway keel boat for a lot of years and has figured out the trick of at least predicting it's behavior.
Where are you?
Unless I get attacked by a Sharktopus, backing out of my slip at the beginning of the trip is usually the most stressful part of the voyage. My boat is heavy 30,000lbs, has a 6' full keel, an underpowered engine (36HP), and a prop in an apeture.
I no longer find her unpredictable in reverse at all. She is in fact, very predictable. The secret, I have found, is in accepting what she can and can not do, and estimating the forces that will be at work before untying.
I'll try and explain. My pivot point is located just forward of my wheel, where the mizzen mast is. That means that all windage forward of that will try and blow the bow off. In fact, there is so much forward windage, that my boat apparently heaves to with a FULL mizzen only, with the 150sqft sail and the forward part of the boat's windage being about equal. So, 40ft of boat, including my bowsprit (which is at the end of the lever) act like a unidirectional-wind-powered bow-thruster. I also know that my LH prop causes the boat to strongly prop walk to starboard. I also know that my rudder will not overcome much opposing wind, and will barely keep up with prop walk if there is no wind.
Knowing these things, and knowing that I can't overcome them, I have to work with them. Before I untie I look at my masthead wind indicator and feel the strength of the wind. I know the wind blowing the bow one way or the other will be the biggest actor. Once I know that, check for current, and account for prop walk. I kind of imagine all these vectors in my head and decide how I can affect them and make a plan.
Often the wind blows from my starboard side. This will blow the bow to port. The prop walk will compound the problem. If I "try" to overcome this in reverse with the rudder, I'll be making an insurance claim. I HAVE to accept the limitations of my craft and not pretend that if I just twist harder on the wheel she'll go.
So, I do something else, like shorten up the starboard bow line, release all others, and release it last so I start backing up crooked, and straighten out as I go. Or I use a burst of forward with starboard rudder to straighten out, then resume backing.
Basically, I know the forces that will act in opposition or unison to affect my steering, and I know and accept that the rudder is a small, not a large player in the overall plan. I imagine the vectors, make a plan, untie my lines and see if I was right.
I hope my long-winded ramble made some sense and helped somewhat....