I think a lot of the suggestions here pretty solid; you can essentially do them all. I ran a similar setup, but it was not double NAT just data capped so I had to toggle my MAC every now and then.

If you do introduce a switch from the wall, you can at least get your gaming devices directly on. You can then run Wifi network off the router for your phone, and WiVRn.

As others have mentioned though these terms are there for security, your WiFi is a risk to the network. If the school is on your side and you are prepared to mitigate that risk by keeping the router updated and choosing strong auth, you could even tune the transmit power and rssi drop off but I have a feeling if they understood you were going to run WiFi and not just a switch they also would have said no.

So this setup could put you at risk of losing internet I guess according to those terms

I had an optiplex like this. I would give the top of the case a couple taps and fans would spin down. No idea why that worked but it did it every time, hurricane winds, couple good taps to calm it back down