I have to disagree with you. I do think it would work, heck it would have to work. If you had the total number of gold coins minted in the United States and the total square miles within the lower 48 States the math would be simple and it would have to work.
However, I just took out my guide to United States coins and found a problem. There are many pages of gold coins listed and to simply add up all the numbers from this book would take a very long time. I may do it, but it does seem like a long task.
3,537,441 is the total square mileage of the United States. I just took that off the web and I am not sure if it includes Alaska and Hawaii but it probably does. What that does say is that there were hundreds if not thousands of gold coins minted per square mile of the U.S. Heck, in just one year, 1928, there were 8, 816,000 double eagles produced. I would guess that most of the gold coins were melted down by the treasury department, and now sit in Fort Knox as solid gold bars.
I hate to admit it, but bad idea.