Its not for 'daily use' ammo, which I store in my safe. Its for the excess crates that wont fit in my safe.
A closet isnt ideal for anti-theft reasons.
So far, building a hidden back plate in my work bench out in my shop might be the best option...
A closet is fine, just don't advertise what you have. Make sure the doors on your house lock behind you and you are done. Again, you're overthinking this. What you want to do (while somewhat commendable ..) is completely unnecessary. If you are in an area that has you that worried about theft, don't keep your firearms or ammo there.