It would be unlikely that anybody would try to build it. Metrics exist to solve some type of specific problem. They are not calculated just to know the answer.
Because different countries have different problems to solve, the calculation methods are not uniform. Even if there were a single world currency, it wouldn't be directly comparable. Now it wouldn't be an apples to oranges problem, but it would be a California Navel Oranges to Italian Mandarin Oranges problem. They are both oranges but are a better fit for some purposes.
There is another issue too. Imagine there is some firm that makes widgets. It provides its own internal financing, accounting, legal and other functions. It may provide warranties and buy options, futures, and forwards on steel. It may sell options on widgets to customers too.
A key element of the United States in the world is to provide services. China, before Trump came along, was a heavy outsourcer to the United States. If another firm only builds widgets and outsources its financing, accounting, legal and other functions, such as logistics, to outsiders, then under your metric the first firm would entirely have its output as part of the metric, while the second firm would ignore the outsourced tasks.
Ignoring the gold element of your question, it would be challenging to even attempt what you are asking.
Finally, China's output is a function of America's tax structure. If the US started paying back its debt to China, it would have to do so in goods and services. American manufacturing would go up and the competition for wages would go up. The fact that China has passed us is at least, in part, a function of our tax policies. That could impact your metric.
After all, if the US really increased taxes, it would not need foreign financing. Cash does not bear interest. China would get a lump of useless cash unless it either bought goods and services from the United States or from a foreign business that was willing to accept dollars for goods and services in lieu of their local currency.
The US has mostly been offshoring dollars since Bretton Woods. The process would have at least temporarily reversed under Nixon, but instead of surrendering one-third of the U.S. gold supply to France and Britain, we went to a fiat currency. As a result of political agreements, such as those with Saudi Arabia under Nixon, the dollar has leaked out ever since.
The US could go back to gold or silver as a standard, but it wouldn't be at today's prices. Your metric would be a problem because gold is not a currency anymore. A gold standard would change the economic processes. It wouldn't look like anything anybody is used to. It would change behavior and so would change your metric too.
I think I see what you want to make, but I do not believe there is a way to do it.
Money is a yardstick of constantly varying lengths.