We can't build ships out of stone, we can't pull them on some mountain away from other ships' cannons, we can't have several layers of planks.

To be fair, yes you can. If you make a large ship dock, build out platforms to the left and right and build up stone walls. Place a behemoth gateway at the end, and some ceilings on top (honestly the ceilings are unnecessary but just in case you want it fully enclosed).

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You now have a garage for your ship. It will be made of stone. It will be (or was pre nerf) pretty strong against any cannon fire.

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You may need some pillars to help hold up the garage structure.

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This would solve your problem.

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