At first, the idea of both of these books seems like a joke in an English class taken way too far. For US, a precocious student with too much Sinclair knowledge dreams up the ultimate way to mock Sinclair: use his own style against him. For The America Play, Parks toys with the idea of taking Abraham Lincoln, widely regarded as the hero of the African-American, and focusing on an impersonator who actually is African-American. The key connections between these two works lie in ghosts/reincarnation, history, and popular amusement.
Both works feature the idea of reincarnation heavily. Bachelder has Sinclair assassinated, which he actually was not, and then brought back to life. This symbolically alludes to Bachelder's own reincarnation of Sinclair and his style with the book, a very meta style of referring to his book within his book. Parks reincarnates Lincoln as a black impersonator, deliberately changing the color of his skin in this "second life."
These books also root heavily in actual history. While some liberties are taken with factual accuracy (Sinclair's cause of death, for example) they both involve bringing history into the modern era, either through grave-robbing or a theme park of historical reenactments and parades. They both handle the situation of how historical figures and history as a general discipline are seen contemporarily.
These books both discuss using history for popular amusement. Bachelder includes a fabricated correspondence regarding a role playing video game in which players dig up historical figures who then come back to life. Parks sets her play in the Great Hole of History, a reenactment site popular for honeymooners. In both cases, they implement history into popular culture, and in both, the results are less than spectacular.