What was integral to the spread of the Enlightenment from Europe to America?
The Enlightenment was a period in history roughly centering on the 18th century, in which traditional authorities were challenged and replaced with more individual powers such as the freedom of religion and democracy. The "original" Enlightenment was a movement in Europe, and so it comes as no surprise that its American counterpart was delayed by several decades.
It bears remembering that the Colonies were never intended to be comparable, let alone rival states, to mainland England. Their exact status was never fully resolved before the American Revolution, but they were meant to function more as corporations; this was evidenced by the way in which American education and medicine lagged behind European contemporaries' for several years after the Revolution, and why works such as those of Washington Irving were applauded as much for their content as for their evidencing of a unique American identity. One of the earliest issues for those identifying themselves as Americans was how to distinguish their identity and culture without relying on secondhand imitations of European models.
During the Colonial period, the Colonies had few functioning intellectual centers of their own, nor were any of them truly leaders in philosophy. The majority of the concepts of the Enlightenment were made available to the American public in three ways: via the frequent importing of European books, through a select number of intellectuals, and through printing. In short, a small number of highly-educated American intellectuals and patriots, such as Paine and Jefferson, voraciously consumed Enlightenment literature, discussed it amongst themselves, then distributed these ideas mixed with their own via the printing of pamphlets or newspaper articles that disseminated throughout the colonies. The original books were themselves frequently circulated as well.
So, I don't think there's any one answer to what was integral to the spread of the Enlightenment. We might also suggest that the diversity of the colonies was essential, because these differences and the problems they created were directly addressed by the freedoms that the Enlightenment advocated.
In America, the colonies were growing, with schools and colleges everywhere. More colonists had access to the latest consumer goods and also the latest ideas circulating in Europe. Through outposts like newspapers and social gatherings, the Enlightenment quickly spread through the colonies. This was also due to increasing literacy rates. The Enlightenment was a burst of intellectualism, rationality, and science. It also inspired the American Revolution for independence.