SUCCESS!!! (except for making it modal. I looked at the code in Show that handles modal-ness and my eyes kind of glazed over ... any insight into how that stuff works would be appreciated! :o)) The following does pretty much just what I wanted. Only slight problem is where the TL pops up -- a little more research in how how the PopUp stuff handles "make the thing pop up HERE" and I think I've got what I was looking for!

Meta question: is this worth cleaning up and turning into a real widget, or should I just go back into my hole and use it for my app?

#!/usr/bin/perl

# Test to see if we can make our own multi-column menu out of
##  a toplevel and radiobuttons

use strict ;
use warnings ;
use Tk ;

my $mw = MainWindow->new ;
$mw->Button(-text => "Make menu", -command => \&GenMenu)->pack ;
my $picked ;
$mw->Entry(-state => 'disabled', -textvariable => \$picked)->pack ;

MainLoop() ;

my $menuselect ;
my $TL ;
sub GenMenu
{   $TL = $mw->Toplevel ;
    for my $f (1 .. 3)
    {   my $frame = $TL->Frame->pack(-side => 'left');
        for my $menu (1 .. 5)
        {   Radio($frame, "Column $f, Row $menu", $f*5 + $menu) ; }
    }
    $TL->focus ;
}

sub PickedMenu
{   $picked = "You picked entry $menuselect" ;
    $TL->destroy ;
}

sub Radio
{   $_[0]->Radiobutton(-text => $_[1],
                       -value => $_[2],
                       -variable => \$menuselect,
                       -indicatoron => undef,
                       -command => \&PickedMenu)->pack(-fill => 'x') ;
}
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