For others that are predictable like this, I push my downloads through a script before they hit my player. Back of the envelope zsh example to scrub first and last minute:

    for f (*.mp3) { mp3splt -d new -o @f $f 1.00 EOF-1.00 }

mp3splt¹ doesn't re-encode files, and as such is neither lossy or slow.

1. http://mp3splt.sourceforge.net/