(OP here, I just don't have my login on this machine)

Shortly after posting, I did find a solution of sorts, here on Perlmonks, of all places. With some modification to the code found here: Non-blocking Reads from Pipe Filehandle, I was able to make a short example GUI program that seems to work.

#!/usr/bin/perl

use strict;
use warnings;

use Gtk2 -init;
use Win32API::File qw[ GetOsFHandle ];
use Win32::API qw();
use IPC::Open2;

use constant ERROR_BROKEN_PIPE => 109;

my $PeekNamedPipe = Win32::API::More->new(
    'Kernel32', q[
        BOOL PeekNamedPipe(
            HANDLE hNamedPipe,
            LPVOID lpBuffer,
            DWORD nBufferSize,
            LPDWORD lpBytesRead,
            DWORD *lpTotalBytesAvail,
            LPDWORD lpBytesLeftThisMessage
        )
    ]
) or die $^E;

sub nonblocking_readline {
    my $fh = shift;
    my $osfh = GetOsFHandle( $fh ) or die $^E;
    my( $bufsize, $buffer, $cAvail, $read ) = ( 1024, chr(0)x1024, 0, 
+0 );
    $PeekNamedPipe->Call( $osfh, $buffer, $bufsize, $read, $cAvail, 0 
+) 
        or $^E == ERROR_BROKEN_PIPE or die $^E;
    return if $^E == ERROR_BROKEN_PIPE;
    my $eolPos = 1+index $buffer, $/;
    return '' unless $eolPos;
    sysread( $fh, $buffer, $eolPos ) or die $!;
    return $buffer;
}

my $cmd = 'bc.exe';
my ($reader, $writer);
my $pid = open2($reader, $writer, $cmd);

my $w = Gtk2::Window->new();
my $vbox = Gtk2::VBox->new();
my $l = Gtk2::Label->new();
my $i = Gtk2::Entry->new();
$w->signal_connect(destroy => \&cleanup);
$i->signal_connect(activate => sub {
    my $text = $i->get_text();
    print {$writer} $text . "\n";
    print STDERR ">>> $text\n";
    $i->set_text('');
});

Glib::Timeout->add(100, \&update_label);
#Glib::IO->add_watch(fileno($reader), ['in', 'hup'], \&update_label); 
+# blocks
    
$l->set_text("init $pid\n");

$vbox->add($i);
$vbox->add($l);
$w->add($vbox);
$w->show_all();

Gtk2->main();

sub update_label {
    if ($reader) {
        my $read = nonblocking_readline($reader);

        if (length $read) {
            chomp $read;
            chop $read;
            print STDERR "<<< $read\n";
            $l->set_text($read);
        } elsif (not defined $read) {
            cleanup();
        }
    }
    return Glib::SOURCE_CONTINUE;

}

sub cleanup {
    kill 'TERM', $pid; # XXX
    Gtk2->main_quit;
}
[download]

This program puts up a small GUI window and sends the contents of the input field to the background process (which is bc.exe from here), and puts the result in a label.

You can observe that the GUI is responsive by pasting an expression that takes a long time to calculate (e.g. scale = 20; a = 0; for (i=1; i < 1000000; i++) { a += 1/i^2 }; sqrt(6*a)) and dragging the window around.

Glib IO watchers don't work here either so I had to poll the reader pipe in a Glib timeout, which is not optimal. But still, it's better than nothing.

Thanks, BrowserUK-from-10-years-ago and BrowserUK in the present!