Importantly though, the roads you listed do all serve a NPS facility and this is a basic requirement for inclusion in the National Park Highways system even as maintenance by NPS is not.
Montezuma Canyon Road is the main road to and through Coronado National Memorial. Minaret Summit Road is the road to Devils Postpile National Monument. And the Mormon Emigrant Trail is, um... hey yeah, why is that in there given no NPS facility is involved?