Hehe... I figured out a use for \"aString"..__ after all. Note that it is not equivalent to 1..1. (Hint: '__' != 1)

#!/usr/local/bin/perl

$t = tell DATA;

while (<DATA>) {
  if ($r = \"aString" .. __) {
    last if $r =~ /E/;
    print;
    $. = -1;
  }
  seek DATA, $t, 0;
}

__END__
Just another Perl hacker,
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If you run this script, you might want to do so in the background. It takes a while to finish...