Again, however, I suspect that that won't really work either as it discards all information that it doesn't need.

You probably just want to build a handler onto HTML::Parser:

#!/usr/bin/perl -w

use strict;
use HTML::Parser;

my $in_table = 0;

my $p = HTML::Parser->new(
   default_h => [ sub { print shift unless $in_table }, 'text'],
   start_h   => [ sub {
     shift eq 'table' ? $in_table++ : $in_table || print shift
   }, 'tagname, text'],
   end_h     => [ sub {
     shift eq 'table' ? $in_table-- : $in_table || print shift
   }, 'tagname, text'],
);
$p->parse_file(shift || die "Need a file") || die $!;
[download]

Tony