Surplus or non-admitted means its not backed by the state if the insurance company goes broke. Ideally you would want a policy guaranteed by the state, but given your situation thats not realistic. So what you want to look for is the company's am best rating. You want an A X carrier minimum. A denotes the carrier's strength as far as stress tests goes, in terms of having proper reinsurance and things like that. and the X (roman numerals) denotes the amount of assets that they have in reserve for catastrophes.
Lloyd's of London is a common underwriter of surplus lines policies. They're the people that will insure things like an athletes arms or a models legs.
What area are you in? I'd recommend approaching an independent agent near the location, there's a much better chance they'll have an admitted carrier that likes to write there. And overall should be more knowledgeable about carriers appetites in that area.