If it were my car, I would be taking a pencil rubbing of those body numbers, getting the casting date and the numbers off the pad and pan rail of the motor if it has it, and the number from the trans!
My last '68 had the VIN or portion of it on the lip that attaches to the bellhousing on driver's side. Later cars have it on the oil pan rail pad.
Good point on the insurance issue. A sharp claim inspector would verify via VIN the car was the one insured, unlikely they would pay if they saw no VIN or a fake one. The agent could be asked up front but you might not want to hear the answer.