Just replying to say that I (sorta) fixed this by going directly to the Amplifi's internal settings menu (via the router's local IP address in browser, not the Amplifi app). I enabled "Bypass DNS cache" in the router settings, and then enabled the DHCP server on the Pi-hole itself. Pi-hole is now correctly classifying traffic in the event log, and I've got the side benefit of also use the local DNS to create custom domains locally for my other devices.
I'm still having the original problem every time I restart though, but I've made a new topic to ask specifically about it because I'm not sure if it's too different to continue asking about in this thread.