Being one of the resident gun aficionados on OF, I can tell you in the gun world any closed container is extremely dangerous to metallic objects, even with moisture absorbing materials. The biggest reason is that the padding and foam materials are not absolutely dry in the first place, and now your sealing off those contents plus whatever you put in it, including moisture bearing air. Second, as mentioned above, the padding and foams are synthetic and have lighter elements that vapor off over time, especially in warmer climates. In this case, it will happen inside the container. Pelican style containers and such are primarily transport cases, not storage cases, and should be treated as such.
The BEST option for storing guns or watches is a fire&security safe, big enough for everything and heavy enough not to move. Many would be surprised to find that safes are not airtight, and are designed that way in order for airflow to keep everything nice and stable. Many safe owners use a specially designed heater stick to ensure the internal temp is a few degrees above ambient to prevent condensing moisture.
Banker boxes are good only if there is a/c in the bank on off hours, and in the vault AS WELL. Many banks do NOT have forced air through the vault, or only have airflow during open vault hours. Otherwise, you are subject to whatever environment occurs when the bank is closed.
Again, using guns as an example, I literally cannot count how many times over the years I have seen damaged finish and rusty guns come out of gun cases and bank boxes. If you have big $ in watches, as it appears in the example above, a safe is a worthwhile and relatively inexpensive investment.
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