In a comment, John Lawler wrote:

To answer the first question, "correct" doesn't mean anything in this context, but yes, it's grammatical. You're also right that this is a better placement for she had; a major reason is that she had is a reduced relative clause, but only two syllables, so it has to be placed away from the other 2-syllable constituent, died away, since they're both crucial. The sentence is overcomplex -- if you find yourself worried about grammar, write a simpler sentence, e.g, Her already scant motivation for talking to this wreck of a man died away entirely.