You are right that the tidal rip through the channel will be extremely fierce, in fact the island and edges of the channel will experience substantial erosion as a result so expect the channel to widen rapidly in geological terms. Even hundreds of years would make a difference, thousands of years certainly would.
The thing is though there is always a period where the water levels on each side are equalized, "slack tide". This will normally last for 1 to 2 hours on earth, in your case it would depend on the length of your day and the orbit of the moon but I would expect it to be similar.
This image illustrates it for you. You have periods of high and low water with the current also ranging between a flow in one direction and a flow in the other. At the point in the center of the flow curve you have "slack water" and at that point ships are safe to manoeuvre. You would need a sheltered harbour to keep ships out of the currents and as you say rips, whirlpools, etc would be fierce in the area.
So ships would time their passage with their tides, using the current to carry them close but arriving during slack water. They would come into dock and make sure they were secure before the tides picked up again.
To leave again they would head out during slack water but timed for when the tides are going in the right direction. As they head out the increasing tidal flow would push them along.