A lawyerly second inaugural, or a piece of the president's heart? Or both?

I am generally chary of literary analysis that finds meaning in sound -- variations of rhythm and meter, assonance and alliteration, etc. But purely by accident, while reading Ronald C. White's little ode to Lincoln's Second Inaugural in today's Times (this by a man who I see in the bio line has written a whole book about the speech), I was struck by the beauty and, as it were, aural authority of the speech's final phrasing as White quoted it:

By contrast, Lincoln disappeared in his second inaugural. The speech contains the word “I” only once. Lincoln was pointing beyond himself to the future of the American democratic experiment, “to do all which may achieve and cherish a just, and a lasting peace, among ourselves; and with all nations.”

Following the qualified, conditional assertion that the nation has endured God's wrath, and the injunction to "bind up the nation's wounds," this final phrasing does, it seems to me, deliver a kind of aural balm.  It chimes internally in multiple ways: in the alliteration of "achieve and cherish," the assonance of "achieve" and "peace," the double nail-down of just and lasting, lightly punctuating the soft susseration of "cherish...peace...ourselves, nations."