Actually, that setup isn't bad, as long as it is considered only as a Sacrificial Stem. Saves much Fiberglass repair resulting from bad docking, or from overtaking a Sailboat in a most inappropriate manner.
My Beneteau has the twin Rudder setup, so I don't have propwash to play with.
Well then, blip the throttle, try to get some sternway, and then attempt any directional control. Propwalk is so much fun, when you have ten feet of beam in eleven feet of berth. The previous owner had simply installed dock rollers. I could see the slight gelcoat grunge lines.
I learned the Spring line trick a long time ago, but I learned that it was better to start any Bumpy Boating adventures Bow first, which means swapping Bow for Stern either after the last trip, or before the next trip, or sometime in between, just by using the docklines. I hardly ever fall in.
An Electric stern thruster would be just dandy, because I can hang the damn thing off of the folding swim ladder, and pull it up when not needed. I'll tell people that it is a Kelp Cutter.
The trick is this: You have forward and reverse thrust, and angle. About Angle: not 90 Degrees CW, but some angle that not only prevents slamming Portly into the dock, but that also, with the main prop, generates a combined Vector Force that pulls the stern out cleanly. Maybe 80 Degrees. This would need some experimentation.
Attaching it should be easy: some Research Grade Velcro, (Yes, there is such stuff. They used it on the Space Shuttle. We used it for securing LN and LHe plumbing. Very strong stuff.), and run the cables right to the Starting Battery about 2 Meters inboard. I can use the hole previously drilled for the LORAN Antenna; it's unlikely to ever see any use otherwise.
And it is easily detachable for dinghier reasons.
Now, I can see one big problem here: What to call it. "Propulseur d'Irlande" seems appropriate, and if it doesn't work out, I can always blame the British. All that I would have to mention is "Seagull..."
Erindipity