Well, I don't think I would classify these as "highways." Certainly I have looked into the origins of the auto trails in earlier emigrant and freight roads, but many times these connections are weak. I have actually driven almost the whole Mojave Road from the Nevada line nearly all the way to Barstow. That route never became a highway, and was indeed pretty much only used in the 1870s by the Army. Several auto trails roughly follow emigrant or stage routes, such as US 80 between El Centro and Plaster City in the Colorado Desert of California.
The most sound connection is that of the National Old Trails Road since it was purposely designed to follow and memorialize the old trails by the Daughters of the American Revolution. That road follows the federally funded National Road (1830s, which was based on Braddock's military trail), the Boone's Lick Trail (established by the sons of Daniel Book in Missouri), the Santa Fe Trail, El Camino Real de Tierra Adentro, and what was supposed to be Stephen Kearney's route to California. The last section ended up following the route of the Beale Wagon Road by 1914. [map