I might try doing some articles about this on Wordpress. In the mean time, I tried to sum up White's vision of Medieval America down to its simplest and easiest to explain components, using only the facts--no conjecture or own additions, simply what we know White laid down here. Twitter-sized summaries, trying to avoid any redundancies or jargon (if White invented the term, I didn't use it.)

The Great Plains

The great plains are dominated by nomadic cattlers which combine aspects of Huns or Mongols with the Old West. They use all aspects of the cow for food and material. Though Christian, they tend to have a fundamentalist, Old Testament orthodoxy and make pilgrimages to Rushmore.

The Deep South

Below the Mason Dixon line, races have mixed to a blur. Women hold relatively higher status--running administrations and households. They eat spicy food and wear little garb. Some practice Voodoo. Their subsistence and commercial agriculture is a diverse array of New World crops.

The United States

The US government has morphed into something similar to the Catholic Church, only headed by the Supreme Court, and based in former National and state capitals. They offer salvation and social services. The US Navy is a maritime republic composed of the Northeast coastal cities.

The Desert

The Rulers of the American desert have absolute power, due to intensive building necessary for irrigation. They have harems, eunuchs and (theoretically) celibate soldiers, and build most of Medieval America's monuments. Burro-riding shepherds and goatherds cling to the outskirts.

Western Religions

The western communities, isolated between mountains, have turned to more diverse and esoteric religions. California is Scientologist, the Pacific Northwest is Buddhist, and New Mexico, some kind of New Age religion. The Church of Latter Days saints has also carved out a nation.

Population 

61 million people or so live in North America. The Ohio River Valley is home to the largest population, and is both a breadbasket and foundry. The Largest cities and trade hubs are New Orleans, Cincinnati, Portland, Sacramento, Philadelphia, Buffalo, and Salt Lake City.

Government

Despite reverting to feudalism and monarchies, rulers still hold historically democratic American titles like "President", "Governor", "Colonel", etc. Likewise, realms are designated things like "State", "Territory" or "Commonwealth." Slavery has returned, but is evidently not by our standards race-based. They appear to be gained through conquering nations.

Warfare

For the most part, horse archers rule the deserts and grasslands, mountains and coastal city-states use pikemen and knights dominate the Heartland. However, heavy cavalry is used by the desert empires and U.S. army. The largest fortresses are in Macon, Meridian, and Rock Island.

Canada

Most Canadians have blurred with their neighbors across the dissolved American borders. Buddhist city states in British Columbia, cowboys in the prairies, and Maritimes conquered by the U.S. Quebec remains distinct and Roman Catholic. Also, hunter tribes dwell in the far north.