Update:

The guys from SCEE were able to fix my connection problems today! YAY!

I've also given them the PSN IDs of everyone else with connection problems I know of:

DeepMix

Tomeru

klocki_LEGO

kanar

leethax21

shibobo


If anyone else is having problems, please tell me, so I can tell them.
SCEE told me that everyone's connection problems should be fixed very soon.

BIG THANKS to Tony, Anuj, Chris and Brian for looking into this (and to everyone else I don't know of).
Now, who's gonna join me for some easy wins - I'm out of training!