In addition to the method you've tried here, the FAQ also provides documentation on closing a filehandle using the syscall directly.

# from perlfaq5
require ’sys/syscall.ph’;
$rc = syscall(&SYS_close, $fd + 0);  # must force numeric
die "can’t sysclose $fd: $!" unless $rc == -1;
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The method you tried didn't work for me either (which makes me wonder why it's in the FAQ), but this one did. Here is the test script I used:

#!/usr/bin/perl -w
require 'sys/syscall.ph';
$| = 1;
open(OUT, ">foo");
&CloseAllOpenFiles();
print "done with close.\n";
sleep 20;
# go look at process with lsof to see if fd still open

sub CloseAllOpenFiles {
  for my $fd (0 .. 1024) {
    my $rc = syscall(&SYS_close, $fd);
    warn "Can't sysclose $fd: $!" unless $rc == -1;
  }
}
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