DMZ seldom works - it isn't a port restriction, which is all the DMZ does - tells your router that to this IP address any type of traffic, from anywhere can be allowed to and from this device. But that isn't what NAT is - it stands for "network address translation" - 192.168.*.* isn't a routeable IP space - it's local only, and can't get out to the internet (for security reasons, and because there's only 65,534 IP combo's for that range, not very many).
The PS3 can tell it's going through two devices to hit the net, which ends up being 3 hops to actually get out of your LAN, therefore the NAT3 rating - setting your router and modem to bridged mode (i.e. PPPoE, rather than dynamic or automatic) has the effect of showing your router as the default gateway out, rather than the modem - that's basically all it is - rather than having to go through 3 hops to get out (LAN, internal gateway, external gateway) you're only going through two (LAN, external gateway). NAT1 would be directly connected to the modem itself.
Hope that makes sense.
edit: if you haven't found a "tutorial that works" it's possible your modem/router combo don't support bridged mode - either that, or you've missed a step, the tutorial was incorrectly written, or it wasn't specific to your hardware. Do some searching on your specific router, and your specific modem, and you should be able to find out if its possible - it isn't always; depending on the limitations of your hardware. Mode DSL modems DO support bridged mode, however, because it can cause problems with all sorts of things if you need it (remote access, internal web or ftp server, online gaming, etc...)