Steerage in your case is only applied with thrust, and in your case thrust aft of the rudder as its an outboard I dig my outboards in and trim down approaching the berth, leaving them up will push the bow up and indeed more bow out of water is more sail. The suggestion to TRIM DOWN is the best one I see, and speed is your friend. We often see what you're describing on larger ships with a large sail area. As we approach the berth and slow down the effect increases. Mitigate this by aiming high and allow for the set, even giving the odd "bump" with full helm before engaging ahead or astern (more effective trimmed down also) opposite rudder slowing the ahead speed and drifting transversely.....bodily.
Hope that makes sense, it does not make sense to me to add additional rudder etc, and we're not going to add a bow thruster

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There's a lot more to this including how the pivot point moves around, (to the bow with speed) and as you slow it moves aft. Just shifting weight forward would help too but the dynamics of the pivot point being at the bow when moving (that being 3 knots?) and moves to the stern when stopped are fundamentally what you're fighting. Ultimately they all back to the wind.
Hope this helps