I fail to see how greater and earlier inclusion of Francophones, Hispanophones and (later) Lusophones into America would negate this trend. In fact, I tend to think that a more linguistically and ethnically diverse initial population leads people to be more accepting of multiple languages. USAO's America embraces Spanish due to the acceptance of Simon Bolivar as a founding father who likewise embraced the American system; French was adopted by the elites of high society, especially those of an artistic bent; and Portuguese is rapidly becoming a new aspect of a polyglot mixed language that is forming, at least so far.
These aren't overnight changes, nor were they sold as such. People can be remarkably resistant to change. But a racially integrated centennial America is feasible, in these conditions.
Even if the US never annexed Mexican Territory, let the Confederacy go, shipped the rest of the blacks to Liberia, declared the Indian territories to be independent nations, expelled all remaining Indians to those territories, and advanced integration of the German and Irish minorities 50 years faster than in OTL, the US would not be racially integrated by the centennial.
Incorporation of minority groups whether racial, religious, or ethnic has been a slow and tension filled process. Adding large numbers or additional minorities would increase those tensions and delay, not speed up integration.
You're forgetting one of the major ideologies in the 19th century - Nationalism. Multi-ethnic nations such as Austria faced increasing internal divisions as the various ethnic groups, typically defined by language, agitated for their own autonomous nations. Meanwhile, the long fragmented Germans worked towards unification.
A multi-ethnic nation forming across North and South America in that era would require a fundamental change in the view of nationalism. It would be easier to get 19th century Britain, France, Spain, and Portugal to unify than for all of North and South America to do so.
The Anglophone nations of North America showed prejudice against other Anglophones. Englishmen faced prejudice in the US at least until the 1850s. The Irish were often seen as non-white until at least the Great War. Many Confederates considered themselves a separate and superior race to the Yankees.
Most Hispanophone nations of Central and South America showed no desire to unite with other Hispanophone nations, let alone Anglophone nations. The only exception was Central America, but the Federal Republic of Central America (1823-40), the Confederation of Central America (1842-44), Federation of Central America (1852), the Greater Republic of Central America (1896-98), and a second Federation of Central America (1921-22) all collapsed back into their constituent states. Nothing larger was attempted, let alone succeeded.