Hire a great agent - if you've got one, great, let her do her due diligence. An offer supported by the facts of the market is the strongest case you can make. The better and more accurately aligned your comps are the better your analysis - and for a unique property it can be tough. But once you pull it together it will guide you well. The seller should be receptive to the facts, but there is not guarantee of it, as Deb points out.
Your best case will be made by having your agent present in person a complete offer supported by the facts. I like to begin that conversation with the seller with "let me show you why we think our offer makes sense....". If they listen, you are on your way. If they don't then they are not realistic and your chances are slim.
Good luck to you,
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