I've got it working now! As before I've removed most of the code from my program.

use Tk;
use Win32::API;

...

# Windows constants
my ($OnTop, $NoTop, $Top) = (-1, -2, 0);
my ($SWP_NOMOVE, $SWP_NOSIZE) = (2, 1);

# 'always on top' state
my $isOnTop = $NoTop;

...

# Create a Win32::API object for SetWindowPos
my $SetWindowPos = new Win32::API("user32", "SetWindowPos", [N,N,N,N,N
+,N,N], N);
# and one for FindWindow
my $FindWindow = new Win32::API("user32", "FindWindow", [P,P], N);

...

my $w = new MainWindow;

...

my $aotCBut = $w->Checkbutton(-text => "Always on top",
    -onvalue => $OnTop,
    -offvalue => $NoTop,
    -variable => \$isOnTop,
    -command => sub {
        # get a handle to the toplevel window containing our Perl/Tk a
+pp
        my $class = "TkTopLevel";
        my $name = $w->title;
        my $NULL = 0;
        my $topHwnd = $FindWindow->Call($class, $name);
        if ($topHwnd != $NULL) {
            # change 'always on top' state
            $SetWindowPos->Call($topHwnd, $isOnTop, 0, 0, 0, 0, $SWP_N
+OMOVE | $SWP_NOSIZE);
        };
    })
    ->pack(-side => "bottom", expand => "yes", -fill => "x");

...

# start the UI
MainLoop;
[download]

The Win32 FindWindow API call will return a handle to a window with the specified title and class. Perl/Tk creates windows of the class TkTopLevel. You must call this after the window has been mapped (i.e. after MainLoop), otherwise you won't get a valid window handle.

A useful reference when using Win32::API is here, it talks about Visual Basic but you can fairly easily convert it to Perl.

--
Kevin O'Rourke