If I were licensed in NM (and there) I'd love to take a crack at this for you. I've done work for and against insurance companies and know how their people think...I wish I didn't.
Anyhoo, as Tony mentioned, a "stated value" policy should be no problem, but I sense you have an ACV (actual cash value) policy. That's where the fight will be if you have one. They will find 2 or 3 cars they think are similar to yours in condition and tell you what the value is. You will have to prove that your car is worth more. Your receipts are only of value to prove the condition of your car. Don't expect to get back what you invested in money and time. That is almost irrelevant.
Think of it this way. If a guy was to go to a dealership and buy all the parts to build, say a '97 Grand Am (much like my new, used work car), by the time he had all the parts and time in building it, he'd probably have $50,000 into it. However, you can buy a very nice one for $6,000. ACV is not what was spent, it is the value of the completed vehicle on the open market. Likely, the ACV of the "new" Grand Am would be $6,000 plus a credit of some sort for no miles and all new parts (because you would not find a true "comp"), but probably not even $8,000 in total.
In your situation, the age and relative rarity of the car only changes the process of determining comparables. The concept is the same. Likely, you will have to find very nice comps with verifiable prices paid (classic car auctions?), then get as much information about those cars as you can so you can show that your car is worth more than those based upon some objectively verifiable criteria. That is where your receipts come in handy.
I would start the research now, but see what the insurance people say. Although a great portion seem to be spreadsheet reading, corporate minded, non-enthusiast, drones, you will find nice, reasonable people out there. You can't judge the company at this point based on one drone's attitude.