That would be a grand experiment indeed. One trick would be to accurately measure and keep-honest the GDP numbers. I'm all for drawing a curtain between the Fed and States on this.
The idea came from a friend. His original suggestion was that the it be based on the number of adults living in the state - a poll tax. E.g. $10,000 per adult. That would effectively eliminate any possibility of evasion. I objected because it is regressive - poor states would pay a higher percentage of GDP than wealthier states.