A different idea that is simpler. My slip has fixed pilings and pier. On either side of the slip, I have buddy or assist lines tied from the outer pilings, parallel to the slip to the pier cleats/pilings. In situations similar to yours, if I have crew, I instruct the crew to get a bow line over and around the windward buddy line and to cleat it off. Now the bow can't fall off and I can control the stern relative to the slip using the engine and rudder and power slowly ahead to get into the slip. I will be adding the SJ Johnson "Grab and Go" hook to that mix. The grab and go hook is held onto a boat hook using friction and a specal bracket that attaches to the boat hook. The crew simply uses the boat hook to position the hook onto the line, and then pulls back on the boat hook to release the hook from the boat hook. The hook has a two way spring loaded gate that will prevent it from falling off the line if you get slack in the line.
In your case, you have a floating pier so you have to use a different arrangement to simulate the buddy line. I suggest that you try this. Tie a line from the forward most cleat on the windward side of the slip back to the aft most cleat on the windward finger pier. To make the hook up, the line needs to be supported off the deck so crew can engage the hook easily. To to this, fashion a flexible standoff at either end of the line using large diameter vinyl tubing. I'd use a slightly undersized slot in the end of the vinyl tubing so that under load, the line can be pulled free. Attach the dock end of the standoff permanently to the dock. I recommend doing it horizontally into the slip so as not to create a tripping hazard in getting on and off the boat. If the boat should ever come into contact with this arrangement, the standoffs will deflect and should not damage the boat. This arrangement is more or less permanent as it has to be in place before it is needed.
Now, when approaching the slip bow first in the crosswind, helmsman's first job is to get the bow close enough to this buddy line so crew can make the hookup using the Grab and Go device and boat hook. Once hooked up the crew can quickly cleat off the line at a premarked point to the bow cleat. Now, the bow can't fall off and you control the stern with the engine and rudder. As you move forward, the hook simply slides along the line, always holding the boat at the preset distance from the pier.
This device is useful for departures in a similar manner. To disengage it, you simply slack the line and use the boat hook to grab a flexible ring on the hook and pull the hook free. The Grab and Go is somewhat expensive for what it is, but well worth the price in my opinion.