I'm having the exact same problem here.
1. Read about Advanced DMZ and thought I had finally found the solution to my problems with the HH3000. Enabled it, nothing. My 3rd party router kept the private 192 address even after releasing, renewing and rebooting (it's an Airport Extreme, latest model).
2. Saw this thread, realized I was on an older firmware and rebooted the HH3000 to try and get the new one pushed to me. That didn't work so I did a factory reset of the HH3000. That also didn't work, and broke TV service so I called Bell. When they were trying to resolve the issue I requested an upgrade to the latest firmware, which they did. Now it's on FW version SG48221028.
3. Tried Advanced DMZ again. This time the router was able to grab a public IP, but I got the same issue as MerceanCoconut. Nothing works, nothing is accessible. Flip back to regular DMZ and once it grabs the private IP again, everything works. Tried multiple reboots and resets, as well as an additional factory reset with the new firmware. No luck.
Not sure where to go from here. I have a technician coming to try and fix the TV service issue. I was going to ask for a new device, hopefully I get someone knowledgeable.