Hi once again!
Our problem, as it stands today, is solved. We ended up trying to install the FOG server on the same subnet with the host machines, which worked. After that we tried putting the machine back on the subnet where all our VMs are located. That broke it. Later the network admin realized that during his configuration he accidentally left a space after the IP on option 66. After that was fixed things stated working out.
So in the end what I was chasing was a typo.
A big thanks to @george1421 for being as helpful as You could during the troubleshooting process.
I am now happily deploying my Windows 10 images.