My car is insures thru Heacock Classic. They insures the car with the previous owner. They have the 3000 mile limit also, but I have not been asked to verify my actual mileage. It's not a problem, I'm under 1000 a year so far. I looked at another classic insurer, but their information made it sound like I could only drive to car shows only.
My policy allows pleasure driving (the whole point):auto:, so it is a second car. Also, the car must be garaged in a secure location, ie inside. The cost is reasonable. PM for contact info.
Good luck.