The only way I can think of to possibly insure a car like that would be through a specialty carrier. You could possibly insure it at what is known as "Agreed Value" instead of Actual Cash Value.
Agreed Value is where you basically determine, usually through some kind of mechanic's statement or appraisal, what the vehicle is actually worth and then submit this to your insurance company. As long as everything looks good and meets their guidelines, that's the amount they'll pay out if the vehicle is totalled.
Usually, this type of coverage is used for restored classic cars, and probably show cars too. The downside is that there will probably be mileage limitations and possibly even age limitations. I don't know how they will feel about the whole engine swap issue either.
http://www.hagerty.com and
http://www.grundy.com are two big companies I can think, but I'm sure there are a ton more.