NYC Firearms Registration
If a thief were to discover an entire shotgun, it would likely become a trophy of his efforts. A partial shotgun, unusable in it's discovered state; perhaps not. If you take the time to disassemble your shotgun, you may as well take the allowable pieces home with you. Any measure of discouragement to theft is better than none.
You may keep your parts, but not all of them. The barrel, buttstock, forearm, etc. is allowed, without registration or permit. The receiver, and only the receiver, is restricted. If posessed in NYC, it MUST be registered with them.
As you probably already know, the "permit" will set you back one full morning, part of the afternoon, and approximately $235.00. There is no additional "cost" to register your rifles and shotguns, although they MUST be registered.
Storage units are very cold in the winter, hot in the summer, and interior temperatures change rapidly here in the Northeast. Dampness and condensation are your firearms' enemy. Storage units are generally uninsulated steel/aluminum boxes with concrete floors.
Where will you be using them? Do you have a reliable friend/relative/hunting partner outside the five Boroughs with whom you can store the receivers? In their secure home, can you store the entire firearm? I'm not too fond of the idea of unsupervised storage of firearms, like a rental unit, so I suggest the home or business of someone you know. Sucks to have restrictions such as these to deal with, but you do what you must.