Generally speaking, any device ("server") hosting a "service" NEEDS to be assigned a static IP. It simplifies routing significantly and avoids random break problems because DHCP is incredibly stupid at times....
Is there any specific reason you need DHCP to assign an IP to your main hosting server vs setting it all statically?
Moving it to it's own system will not fix the routing problem. You can probably still leave it on the USG.
You should be able to set a fixed static IP on your server, and then also statically assign that same IP to your server in your USG DHCP config- as long as they both are "thinking about" the same IP I think routing should work correctly.
If that breaks, try just assigning the static IP only from the USG side or only from the server's side. I'm 90% sure that even if the USG does not have your server machine in it's client list, if it sends broadcast packets to an entered IP looking for the unifi server, and the unifi server is listening on that manually set IP, they should be able to talk.
disclaimer: i am high as shit right now and this may be bullshit