I would like to suggest a structure that can be added to boats, unique per vessel, that can vary based on the size of the ship. The structure can be an animal pen that has limited space, each tame will still be counted toward total ship crew but each tame type would count toward a specific amount of space in the secure structure. The structure would need to be on the top deck of the ship.
Example, the structure on a brigantine would have 10 effective animal slots.
An elephant, giraffe or rhino would cost 5 slots. You could safely store 2 large creatures.
A bear would cost 3, so 3 bears.
Horse, cat, cow, bull and sheep would cost 2, so 5.
Shoulder pets and chickens would be 1, so 10.
This would be a way to store creatures for either long voyages or for safety. Each creature gets a unique ID associated with it. The stored creature would drop inventory (except saddle) and would have food storage slots for animals. Their effective weight would still count toward total ship weight, and the structure couldn't be destroyed by the radial menu while it has animals in it. It could still be damaged from PVP and ships of the damned, upon destruction it would release the animals and they'd be relatively injured and/or panicked.
We are losing tames while crossing over zone borders. Tames start to glitch, go through ceilings, fly off vessels or sink to the ocean floor and die. This would prevent a lot of vanishing tames, tames lost at borders or those that end up dying when you are trying to get them on board. Sure, you can build a platform and walk them on board now but if you are out harvesting or adventuring you risk losing them when sending to a ship, or whistling them on to a ship. It's just unreliable and glitchy.
There could also be a variety of stables, barns or other structures for bases where we could store tames. Same damage rules would apply, similar limits. Other games have structures like this where you can store pets, tames, livestock etc, in a somewhat safe place. (Life is Feudal comes to mind)