I am completely astonished that in the tally of what we find lacking in the OP's list, books of music are strikingly absent. The shaping of the country in the colonial era through to independence had much to do with religious as well as political separation from England. The onset of a publishing industry in this period spawned numerous hymnals - in particular the Shape Note format. Northern & Southern Harmony, & the start of denominational hymnals. Standardizing hymns in books helped form an identity, and was part of the trend toward universal literacy in the US.

While some books are compilations of significant songs or tunes that are part of the American heritage, hymnals were, and are, used in a much different way, to direct and inspire. When thinking of influential books- how many of those mentioned are an intrinsic part of someone's life experience? I know there are a couple on that list I've read multiple times.

Let's hear it for early American hymnals, please?

Joanne in Cleveland (whose church life is enriched by 7 different hymnals)