He certainly "used" music he disliked, in his discussion of Wagner in A
Tramp Abroad and I think in an essay or two.  His comments on opera
audiences contain the usual exaggerations, but are sometimes acute.

He makes rather loving fun of the popular musical war-horses of ante-bellum
days (e.g. "The Battle of Prague") in the Grangerford episode of Huckleberry
Finn and the somewhat parallel "House Beautiful" chapter of Life on the
Mississippi.  Life on the Mississippi also includes a chapter of Huck's
story that Twain later decided not to include in the  novel.  In that
chapter a raftsman sings  a verse or two  of a slightly ribald ballad he
liked (about a woman who loved her husband, but loved another man "twice as
well").

See also his  use of a song from "The Mikado" in "The Man That Corrupted
Hadleyburg."  And see the early chapter of Pudd'nhead Wilson where Angelo
and Luigi are presented as European-trained performers of four-handed piano
pieces.

All in all, I suspect the more you examine Twain's writings, the more bits
of favorite music you'll find.

.....In fact, the longer I stretch this message the more I recall--doesn't
he include his own lengthy version/spoof of "The Erie Canal" in Roughing It?

And where is it that he praises highly the Fiske Jubilee singers?--He hears
them perform in Europe and they remind him achingly of his early days.

I seriously doubt you'll find anything as formal as the Faulknerian tricks
you mention--for Twain it's likelier to be casual quotes and allusions.  But
I do urge you to explore his travel books and such as well as his fiction.

Whoops...one more before I shut up.  Is it in the Autobiography that he says
he has always found a couple of lines from "My Old Kentucky Home" haunting
and unbearably sad?

Mark Coburn