When I initially got my policy with Heacock, I had to get appraisals on certain high valued (in my mind at least) cars before they would give me the agreed to amounts that I was asking for. So I went and had an accredited appraiser with the AIA fly in from Virginia to appraise my small collection for insurance replacement value. As I remember, there are three ways to appraise cars, with comparisons of recent sales (fair market value), replacement by building the exact same thing as you have (actual cash value), and the third one escapes me. Obviously we want to hang our hat on the replacement value with an insurance company and there really is no reason they will not accept that either.
If the appraiser will not do such an appraisal, get rid of them and get someone who will do it properly. I'm glad I got the right guy the first time -- it was quite an education for me and all is well.
Now when I signed up with Chartis they did not bat an eye with the amounts that I requested. I was expecting them to say they wanted to see appraisals. Nope, nada, nothing -- they accepted my amounts with no problem. I'm sure different companies deal with the appraisal thing differently so your mileage may vary.