I liked Menzies books but then I respect veteran ship's captains about oceanic travel more than faculty who just navigate the campus library.
On the same assumption the Chinese wouldn't repeatedly cross the Pacific unless there was an immediately compelling economic reason, preferably both exotic trade goods and sizable markets, most of the European colonies along the Atlantic didn't happen either as the gold was inadequate for many years and constantly played out, the crops took years of expanded cultivation (tobacco, cotton, sugar cane, indigo, corns, potatoes, squashes, beans, cocaine, etc.) and sizable infrastructure/farms/ports to become serious cash crops-even lumbering and other mining did too. Losing money on voyages, colonies, military and exploratory expeditions, on seized land without infrastructure was standard results (Alan Taylor's "American Colonies" and David Landes' "The Wealth & Poverty of Nations", Fred Anderson's "Crucible of War", John Steele Gordon's "An Empire of Wealth" all bring out that difficulty of making colonies here pay even 200-300 years after initial discovery. The Chinese focus on building trading stations and accessing customers and high value products rather than conquering militarily any land they found would drastically change the cost and logistics of the Americas, like the Phoenician and Minoan empires, the Portuguese, or the Dutch.
The story of Fu Sang describing a long overland trek by a small Chinese party down what sounds like several thousand miles over 5-8 years including a description of the Grand Canyon, flora and fauna, etc. is quite a ways back as are the many Shang Dynasty elements found with the Mayans (mathematics, symbols, jade, astronomy, etc.), the Pacific Northwest's boats/homes/woodworking etc. that look far more like what stranded sailors would build and are unlike any other NA Native uses of wood (planks) or Balboa's observation of what he thought were Chinese junks on the Pacific side of the Panamanian coast suggest the Chinese did find the Americas a viable market for trade well before Menzies' 1421 book discusses.
Along with the placer gold and minable gold in Oregon and Northern California, the massive ships' timbers of the Pacific Northwest or California redwood trees (that fueled much of New England's trade, not a lot of tobacco exports from Boston or Portland Maine), whaling, corn, sweet potatoes (a major staple in China today), salmon, tuna, or further inland copper, coal, silver, tin, cocaine/coca leaves, chocolate/cacao, etc.) If this isn't sufficient for long distance ship-borne trade, then you don't have a compelling case for European and African trade which in our time line goes back thousands of years with rude commodities and uncertain markets for voyages of many months.
A Chinese trading network with trading posts in Korea, Japan, Aleutians, Alaska, Vancouver/Washington, California, down to Mexico or even Peru seems pretty reasonable, just like everyone else had to set up logistical bases along the best routes. Emigrating populations are usually more despite government choices, the same vigorous families who have the wherewithal and skills for emigrating are middle class, skilled citizens rather than boatloads of the poor (unless that's how you run things like the Pacific Mail loads of Cantonese peasant men organized into work companies and rented for western railroad building and then brought home.) The Chinese had far more people to send out in emigrant communities than the comparatively tiny populations of England, Portugal, Holland, Norway, Belgium, etc. so establishing sizable port cities, farming clusters, overseas armies, etc. would be more within their resources than anywhere in the world at the time. And the Chinese for a thousand years or so had a more sophisticated army than Spain's (longer use of artillery and muskets, integrated cavalry, signalling, Sun Tzu etc. tactical doctrine, logistics from running vast armies in the field, etc.).
