Hola, Fantasmic!
I know that "Hail to the Chief" was available on WDW Forever at one time, I believe as part of a longer track of the show's score.
"Battle Hymn of the Republic" is on the Hall of Presidents LP, which floats around on ebay.
I think the real HoP gem is a score track of the music that accompanies Lincoln's old speech, which they used to play in the foyer. I recently heard the same recording in the American Adventure rotunda, at about 9 pm, just before Illuminations, so it's still doing duty.
Hope this is somewhat helpful.
Jeff in NY