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While I don't have the same situation; I have had difficulty with the boat backing correctly due to an offset prop (massive walk). Here is a procedure that works for us backing the boat out of our narrow double finger slip without handling the boat while standing on the dock.
I first turn the rudder hard to port; as the boat backs hard to starboard with the rudder centered. This keeps the boat backing fairly straight. In the OP situation he would turn the helm hard to starboard to counteract the walk with the rudder.
Before we cast off I have the bow pulled in so it is close to the dock and let the stern line loose so the boat is angled a bit in the slip. All lines are doubled and pulled aboard when we cast off. When we cast off I engage reverse and as the bow blows down it blows down to about the middle of the slip before the boat gets enough way to back up straight.
If my bow is turning left I add a bit of throttle to counteract; if it turns right I hit neutral to kill the prop walk and allow the rudder to work.
In the case of the OP he would want 2-3 kts of velocity in reverse so that when you go into neutral the flow across the rudder will over-power the ability for the bow to blow down. Depending on your rudder you might not need to be hard over; some rudders tend to stall when turned hard to port or stbd.
Once the bow crosses the eye of the wind you will want to go into forward; turn helm hard to port and let the wind blow the bow across so you are motoring out of the slip.
You might try this procedure with the boat walked back one cleat first; so bow line is at the dockside spring cleat. Have some good boat hooks onboard that have good padding on the ends so if you need to push off of your neighbor you can without doing any damage to his boat.
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