Prop walk is your friend and something every skipper has to deal with.
First, I assume you have clockwise right rotation. Second, increasing acceleration will just make things worse so go easy on the accelerator.Third, what I'm about to tell you is hard to visualize sitting at a computer and if you decide to practice do it in a turning basin until you get the hang of it.
BACKING THE BOAT: At my dock I need to back out and have the stern turn to starboard so I can exit the slipway into the turning basin. Here's how I do it. The first part is obvious but the second part isn't. I obviously start with the rudder centered and the engine in slow reverse. Once 3/4 of the boat is in the slipway I use prop walk to my advantage. I put the engine in FORWARD. Sounds wierd but the stern swings slowly to starboard.
Say something is happening in the slipway and I don't have time to fool around. To whip the stern around I'd still stay in FORWARD but I'd turn the rudder to port and goose it. The stern will rapidly turn to starboard.
PORT SIDE DOCKING: Approach the dock at slow speed with the bow slightly angled toward the dock. Center the rudder and put the engine in REVERSE. The stern will swing nicely and easily toward the dock. Here's where skippers get into trouble in this situation. Instead of CENTERING the rudder they turn to port with the engin in reverse. Nothing happens at first so they goose the engine. As soon as they do that the stern turns to starboard. To correct the situation they turn the rudder to starboard and that's when things get really screw up. What they should have done with the centered rudder is NOTHING.
On Catalina Island it is sometimes fun to watch how skippers get into trouble with prop walk. One place is the fuel dock and the other is picking up a mooring. The skipper approaches the mooring a bit too fast. His rudder is centered, which is good, but then he floors it to stop his forward progress. I say to myself, "DON"T TOUCH THE RUDDER" but they always do and that when things go from bad to worse. The skipper then over corrects and it end up being a Chinese fire dril except the Chinese fire drill is better organized!!
Practice in your turning basin to see how the forward and backward motion of your boat is influenced by the position of your rudder.Also see what happens when you goose the engine. If your rudder is not in the correct position things go badly rapidly.