Hi. In my case, my server is also the DNS and DHCP.
In the DHCP settings, my server is the gateway. In this way, all traffic passes through it.
If you use authenticated proxy and the stations are not joined, all pages that are opened will request user and password.
Without authentication, we can not create rules for specific groups. (DIRECTORS, TEACHERS AND STUDENTS).
I’m not an expert, but right now, we have 700 computers through the transparent proxy. I made many tests with the authenticated proxy, but as well as you, it was not possible to connect all equipment to the domain.