"Unsupportable."

If this was called in we'd call it unsupportable as it is what it is. The business setup that we deploy is your router to some wired switch and then from that switch to the APs (wired) which supply the WiFi in each area.

As presented I would expect this to fail.

Even so I can only offer one idea short of redesign and that is to check out what DNS you are deploying. Try others like 8.8.8.8 4.2.2.1 etc.