Since no one has chimed in, I will throw in my two cents.
I would never buy insurance on guns, especially NFA items like a silencer. A machine gun...maybe.
Insurance is a negative expectation proposition, meaning it is like going into a bank, giving the bank $1, and getting back 99 cents. Insurance should generally only be purchased under three conditions: 1. it is a legal requirement (car insurance to drive); 2. it is contractually required (like homeowners insurance to get a mortgage); 3. to prevent ruination (a loss so bad that you will never recover and be able to live at your current position).
As an example, people often buy the stupid extended warranties, which is a form of insurance, on a TV because the TV is expensive and it might break. Never mind that the TV has a manufacturer's one year warranty, or that most TVs, if they have warranty defects, break within the first year of usage, but the insurance on the TV does not meet any of the above three requirements. It might be expensive if it breaks, but it will not ruin you. You are better off putting the money for the warranty into a repair or new TV fund. The extended warranty has a higher profit margin than the TV.
Same thing with gun insurance. Gun insurance is a huge rip off. These types of policies are high margin items for insurance companies.
You might think, well, if I am a victim of theft, at least I will get my money and that is worth piece of mind. True, but you are paying a premium for that piece of mind.
But to answer your question directly, assuming you still want to buy insurance on your NFA item, it is possible to find insurance. You can find a nontraditional route of insurance (for example, Lloyd's will insure anything), or you can have your current underwriter or carrier carve out a special term for you. If they won't, then you just have to shop around. You can find insurers to insure anything.
The trust would have to purchase the insurance, but you can designate yourself as a beneficiary of the policy, so in essence, you are buying insurance for yourself.
As for insuring your silencers, you should be careful. Most policies pay something similar to a market value, NOT replacement value (although you can get replacement value policies, it just costs more, and you should be sure what you are buying). The resale market on used silencers is almost nonexistent. So don't be surprised if you pay for decades worth of premiums, and then when the burglary happens, the adjuster pays you $50 on a suppressor that cost you $500 and a $200 stamp. Surprise!
I personally do not have insurance on my guns. Instead, I use the money, that I would have spent on insurance, on a nice and advanced surveillance system.
Anyways, none of the above is advice, so you really shouldn't believe anything that I've written.