apt: Query installed packages from a specific source

I'm trying to get a list of packages installed which come from my company's private apt repository. This works:

#!/bin/bash
fqdn=$1

for pkg in $(dpkg-query --show | awk '{print $1;}'); do
  if apt-cache showpkg $pkg | grep -q $fqdn; then
    echo $pkg
  fi
done

But running it on a system with ~3466 (dpkg -l | wc -l) packages installed takes 1m45.812s. That's an awful long time to display a "Scanning locally for installed packages" to my users. Is there a better way to do this? --- I tried replacing apt-cache showpkg with apt show to read the APT-Sources: line. This warns about apt's unstable CLI interface and takes 15m35.913s.