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Thanks Ali! Great point about the valuation problem. Since markets for collectibles like LPs fluctuate substantially, that could be a significant issue here.
Hi -- I'm the real estate guru -- in my experience insurers will cover anything and everything. (I knew a guy who collected, I kid you not, corkscrews).
In addition to the deductibles problem Dave pointed out, though, you've got a valuation problem. You'll have to work with the insurance company to detail not only the collection, but the condition of the collection -- for something smaller, they'll probably let you self-declare, but with a large collection, you'll have to work with them to detail what you own and how often it has been played, whether the covers are marked, etc.
That said, if it's precious to you, insure it. I like Dave's approach of a rider on your homeowners' -- check that out.
It's likely that certain insurers will cover your collection. But since it wouldn't be a standard policy, it would probably not be an especially good value for you.
A higher "bang for your buck" approach would be to get renter's or homeowner's insurance, and then make sure you had a rider that covered the value of your LP collection.
Also, do keep in mind that if the value of your collection is near or less than the value of the deductible of your insurance, you will not benefit from the insurance if the record collection is the only thing to be lost.