I know Sebastian asked you quite a few of these same questions but I’m looking at it from a different perspective.
We may need the actual pcap file to debug what is going on. Its best to upload it to a google (or such) drive and then post the link here. That way you can take down the pcap whenever you feel the need.
What is your dhcp server? (Windows 2012 or newer server)?
Before FOG was introduced into your environment, did you already have dhcp options 66 and 67 configured?
In the case of fog, if you have an existing dhcp server don’t have fog install one. The fog dhcp server is intended to be when you have an isolated imaging network and you need dhcp services. If you have an in place dhcp server and its capable use it. You fog install should just be a standard FOG install.
As for the dhcp-helper/relay settings on your router. You only need those if you are running dnsmasq on your fog server. Normal pxe booting you don’t need to touch your routers unless you can’t route between the subnets.