Which OS and board are you using? There are a few errors in the debug log, it looks like systemctl is missing, and the dnsmasq process isn't using the pihole configurations.
What is odd, is that if the domain was blocked by the Pi-hole, you would get a response back that was pinging the IP of the Pi-hole, not a failure to find the host name.
I suspect that you have NetworkManager on that Pi-hole install, and that will cause issues. Knowing what board and OS will help us figure out what the stock configuration is.
And if you can try sudo systemctl -I status dnsmasq and report back the result as well.
Being a bit of a noob much of what I am doing is only half-understood, so I appreciate your patience and further insructions. i.e. how would I determine if the DiskStation is running NetworkManager ?
We don't directly support running in a chroot jail on Synology, that's user supported by the community. None of the developers currently own any Synology devices to test with, so we can't really support what we aren't able to directly test on and develop with.
You probably will be able to get a response from the users that support that in the thread that you mentioned however. Sorry that we can't be of more help, but we just aren't set up to be able to do that.