I had quite the run around when I moved in with some roommates with my PS3 not being able to play online games or connect to PSN. Though the two PS4s were fine, just not PS3, lol. We have a stock crappy AT&T DSL router+modem combo from 2Wire/some other brand and even after putting it into the DMZ over WiFi it wouldn't work. But it would work via wired connection.
My solution ended up being:
1. Disabling WiFi on the AT&T modem/router
2. Plugging in an AirPort Extreme 4th gen (already had one) and putting it under the DMZ zone on the AT&T router
3. Setting the AirPort to handle DHCP and all routing over the AT&T router since it was now in the DMZ and showing a public IP
4. Used OpenDNS for the DNS settings (also used for family filter)
5. Everything now works. PS3 is still wired though since I ran a cable from the utility room, over the wall, under the trim pieces and under the carpet to where the PS3 and AirPort are now sitting. Both PS4s play online flawlessly and can download games in the first go. Same goes for the 360 we have. AND as a bonus I got my old fat PS2+HDD online and working since I finally had a cable there.
The only thing I would consider changing is killing the AT&T router/modem combo and grabbing a simple DSL modem only to go directly to the AirPort to eliminate AT&Ts junk. But I'd have to get it all set up and they probably wouldn't like me. And it all works at the moment.
Your solution may be to get your own modem, and yeah, they probably won't be happy but it can be done and everything would likely be peachy
Cox on the other hand was totally fine when I gave a friend a spare DOCSIS 3 modem I had and an AirPort Express. No problem setting it up and they didn't care it wasn't their equipment. Wish more companies could be like that.