How about using substr to look only in a window around the copyright text, something like (not tested)

my $pos;
if ( $string =~ m{(?=.*\Wcopyright(\W|ed\W)|\s\(c\)\s)} )
{
    $pos = pos( $string ) - 200;
    $pos = 0 if $pos < 0;
}
else
{
    warn qq{Copyright text not found\n};
    next; # or whatever
}
my $date = $1
   if substr( $string, $pos, 400 ) =~ m{\D((?:19|20)\d\d)\D};
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I hope this is useful.

Update: Corrected warning line, I'd mixed double quotes and a qq{...} quoting construct :-/