That is one thing that strikes me as a big potential clue: if it were possible to establish any cultural and/or chronological correlation between jade art styles in China and America, it might help pinpoint when cultural exchange may have occurred.
Now, The collapse of the Shang Dynasty aslo coincides with one of Professor Mike Baillie's worldwide catastrophies (1159BC) detected in the tree-rings worldwide. Here's an article by Baillie:
Did Asteroids And Comets Change The Tides Of Civilization?
Mandate of Heaven
Then astronomer Kevin Pang of the California Institute of Technology (Caltech) noted that 1628 B.C. and 1159 B.C. roughly mark the beginning and end of the Shang Dynasty of Bronze Age China. Both ends of the dynasty featured, according to ancient Chinese texts, environmental disasters - dimming of the sun and summer frosts that caused crop failures and famine. Pang notes also the Chinese concept of "mandate of heaven," wherein a dynasty reigned only as long as it protected the well-being of its people. This notion might have originated in the coincidence of dynastic change and climatic disaster.
Some of these Chinese 'refugees' may have ended up in Mexico and gave a 'boost' to the Olmec civilication, huh?