I don't know If you still have the Nat type 3 issue or not, but I found 2 simple solutions:
1) You said your PS3's iP was on DMZ right? Did you know that both your PS3 and Vita can share that same iP? Manually input the same info into the Vita, but just **remember** that you can only have one system logged on to the PSN with that iP at a time!
2) Option #2 actually worked like a charm for me! I took my PS3 off DMZ and put my Vita on it, and my problems where solved! If your router supports UPnP, then your PS3 shouldn't have any problems connecting to the PSN with a Type 2 connection. The option to toggle UPnP on/off should be located in your router settings. For more information on your router you should contact the manufacturer since every router is inherently different. When you do the connection Test on your PS3 it should say "UPnP Available" and it should have no problems getting a NAT Type 2 since it's plug n play. The reason why I recommend option two(If your router supports UPnP) is because I noticed that the Vita doesn't support it(the option is missing when you do connection test) so the only way to get the Vita to a Type 2 is through DMZ.
There's also the option of opening the ports(PS3 and Vita supposedly use the same ports so the process should be the same), but It's a hit or miss because it depends on your router. I spent a whole day trying to get it to work, but it never did. Good luck and I hope my experience helps somebody else.