It might help if you confirm for everyone the directions of your preferred movements.
I originally assumed you were describing backing straight out of your slip into the fairway, then using the rudder
to turn to port in forward gear
and departing the fairway "stage left" and bow first.
I think it looks like others have interpreted your notes to mean you're backing out of the slip, then continuing to port in reverse -- essentially backing out of the fairway.
We might understand better if you would like to clarify stuff like that.
You could also maybe describe for everyone the way the prop moves your boat now. Now that I see it's an outboard
... propwalk may or may not be a huge factor; usually outboard props are pretty small. Still, it's worth a shot since every little bit may help. With rudder amidships, does forward cause the stern to slightly move to starboard or to port? With rudder amidships, does reverse cause the stern to slightly move to starboard or port? Or does power in forward or reverse cause no appreciable lateral movement?
I was going to mention tiller extensions -- with throttle control, etc. -- but I see the well location precludes use of something like that.
Once you figure out the best way to do the maneuver -- what Raku and other have said: practice.
A dicey engine's a non-starter (pun intended).