Here's what I have. It works, but it puts an icon in the system tray while it's doing the calculations. Any idea about how to get rid of that? My googling turns up nothing. I tried a Dialog instead of a toplevel window but dialogs stop everything and require the user to click a button to proceed. It looks like that feature can't be disabled.
It's also pretty slow. It takes about 3 or 4 seconds for 500 rows. I'm thinking about how to speed it up but I'm not sure.

use strict;
use warnings;

use Tk;
use Tk::TableMatrix;
require Tk::Dialog;


my $mw = Tk::MainWindow->new;
$mw->geometry('1000x800');

# TableMatrix
my $t = $mw->Scrolled('TableMatrix',
                        -rows => 500,
                        -cols => 1, 
                        -colwidth => -500,
                        -scrollbars => 'e'
                    )->pack(-expand => 1, -fill => 'both');;


my $width = $t->colWidth(0);
# print "\ncolumn width: $width\n";
$width = $width * -1;


my $heightwin = $mw->Toplevel(-title => 'Height set window');
$heightwin->geometry("${width}x1000-2000-2000");

my $twtest = $heightwin->Text(-wrap=>'word', -width=> $width)->pack(-e
+xpand=> 1, -fill=>'both');

$mw -> focus;


my @tw;
while (<DATA>) {
    my $i = $. - 1;
    chomp;
    
    # $tw[$i] = $heightwin->Text(-wrap=>'word', -width=> $width)->pack
+(-expand=> 1, -fill=>'both');
    $twtest->delete('0.0','end');
    $twtest->insert('end', $_);


    my $endidx = $twtest->index('end - 1 chars');
    # print "end index: $endidx\n";

    $twtest->update; 


    my @dline = $twtest->dlineinfo($endidx);



    my $high = -1 * ($dline[1] + 17);    #do customize '+ 17' based on
+ font size
    # print "\nSetting height of row $i to $high\n";
    $t->rowHeight($i, $high);
    
    $tw[$i] = $mw->Text(-wrap=>'word', )->pack(qw/ -expand 1 -fill bot
+h /);
    $tw[$i]->insert('end', "$i - $_");
    $t->windowConfigure("$i,0",  -window => $tw[$i]); # -sticky => 's'
+,    #put the Text widget in the tablematrix table
    
}

$heightwin->destroy;



MainLoop;

__DATA__
The general budget
1. The Head of the Agency shall provide the Steering Board by 30 June 
+each year with an overall estimate of the draft general budget for th
+e following year, fully respecting the limits set down in the financi
+al framework.
2. The Head of the Agency shall propose the draft general budget to th
+e Steering Board by 30 September each year. The draft shall include:
(a) the appropriations deemed necessary:
(i) to cover the Agency's running, staffing and meeting costs;
(ii) for procuring external advice, notably operational analysis, esse
+ntial for the Agency to discharge its tasks, and for specific researc
+h and technology activities for the common benefit of all participati
+ng Member States, notably technical case-studies and pre-feasibility 
+studies;
(b) a forecast of the revenue needed to cover expenditure.
3. The Steering Board shall aim to ensure that the appropriations refe
+rred to in paragraph 2(a)(ii) shall represent a significant share of 
+the total appropriations referred to in paragraph 2.
These appropriations shall reflect actual needs and shall allow for an
+ operational role for the Agency.
4. The draft general budget shall be accompanied by a detailed staff e
+stablishment plan and detailed justifications.
5. The Steering Board, acting by unanimity, may decide that the draft 
+general budget shall furthermore cover a particular project or progra
+mme where this is clearly for the common benefit of all participating
+ Member States.
6. The appropriations shall be classified in titles and chapters group
+ing expenditure together by type or purpose, subdivided as necessary 
+into articles.
7. Each title may include a chapter entitled «provisional appropriatio
+ns» .
These appropriations shall be entered where there is uncertainty, base
+d on serious grounds, about the amount of appropriations needed or th
+e scope for implementing the appropriations entered.
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