I'm perplexed that no one suggested matching the trailing quote mark. This is really rather easy. This is case-insensitive, is friendlier about white-space and matches the beginning single/double quote with the trailing one. It'll break if the HREF attribute is anywhere except at the beginning of your REF tags.

while ( <ASX> ) {
    next unless m(<REF\s+HREF\s*=\s*(['"])(.+?)\1)si;
    print PLAYLIST $2, "\n\n";
}
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