I think everyone is confusing Aztec with other South/Central American groups. Aztecs and Mayans are always referred to due to their familiarity, but neither was the largest nor the longest-lived group.
If mass migration is the underlying theory of the populating of North America, first across the Bering Strait and then southward and eastward, what would stop a group from leaving South/Central America for undiscovered parts of what is now the U.S.? I would venture to guess that this happened frequently, and undoubtedly semblances of their culture would have accompanied them, because this was all they knew at the time. Either establishing new settlements or assimilating into existing settlements would probably also yield some sort of evidence, just as the Spanish influence was evident here (although theirs was done more by force and eradication).
Further, the physical landscape has changed tremendously over the past 10,000 years, and while there are some historical records depicting the actions of some Central American groups, what was undoubtedly lost will always be the missing link. For example, the coastline of the Gulf of Mexico, particularly in the Big Bend area (Apalachicola to Cedar Key), was 100 miles seaward. Recently, a 7,000 year old Archaic burial site was discovered off the coast, and I have personally witnessed tree stumps located in 40 feet of water, nearly 15 miles south of Dog Island, Florida. To theorize that there is a large number of undiscovered sites that are currently underwater is not a stretch.
As far as mound and effigy similarities, Cahokia is a great example, and so is the Letchworth Mound in Jefferson County, Florida.
Archaeologists may speculate, but few have been outspoken about the connection between the cultures of South/Central America and North America. Much of their research is built from previous assumptions or theories, and when those are challenged, the old guard comes out of the woodwork to defend their turf rather than admit they may have been wrong. The newer generation of archaeologists seem to have a more open mindset, so maybe we'll see some new studies emerge.
This is a depiction of the large mound at Letchworth, and to the layperson it resembles the architecture of South/Central America:
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