@Tycho Okay so I see two things that could be the problem.
Is your Hyper-V network adapter on the same subnet as the FOG server? I’m guessing yes as I only see one scope in your DHCP. In the FOG document that you uploaded, is see this line: All router, DNS, and DHCP setting: No, n in the installation steps.I recommend that some of those settings are actually set to yes. Like this:
FOGDHCPDNS.jpg
Make sure that the IP for your DHCP and DNS servers are set correctly in those first two prompts.
If it still doesn’t work, then please include an image/video of the failure.