Can I ask who your insurer is?
The reason I ask is that I have never been asked to get a car physically appraised. At most, insurers ask for a visual inspection to verify there is no pre-existing damage.
Also make sure you get an 'agreed value' policy not a 'stated value'. The agreed sum is paid out on a total loss, not an adjusted depreciated value. In that case the insurer should be able to quote you based upon your requested 'agreed value' and just visually verify the car has no pre-existing damage, although personally I've never been asked for any proof.
Typical classic car insurers are Hagerty, Sneed and American Hobbyist. I'm with American Hobbyist and they were also the only ones that didn't want another full premium on the 2nd Pantera, when I recently requoted. They also automatically increase your agreed value by 2% each quarter.
Julian
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