Out of interest, I tried to reproduce your setup, and the results are indeed interesting. The only difference is that a 2200x1600x1 TIF file I created was rather more 400K , but that's it. ImageMagick's convert command, $ convert -resize 1024x768 -depth 1 1.tif 1.png, took 0.8 seconds on my machine.

I don't know Imager, but I tried Prima with this script, and the same conversion took 0.07 seconds. Here's the code:

use strict;
use Prima::noX11; # for cgi environment
use Prima;

my $i = Prima::Image-> load('1.tif');
$i-> size( 1024, 768);
$i-> save('1.png');
[download]

And the output is also 1-bit PNG.