i'm back, on PC, and just soloed Bronze! (is Origin broken?)

To answer your question: yes, origin is broken and a total POS . It's usually called lolorigin in this part of the forum ... 
Now for some more constructive advice : the simplest trick for circumventing lolorigin's stupid pairing is to start a lobby on a fixed map/enemy/difficulty (I usually go for London/Collector or Geth/Platinum) and have your friends join through Quick game with these exact parameters. 99% of the time you'll find the correct lobby.

Since you already have a PS3 EA account you should make sure that it's linked to your Origin account on N7HQ - it helps because if your origin account is brand new you'll run into a whole bunch of problems. I know this works because it's the method I used with my alt account.

Also make sure you've installed all the dlcs (Resurgence, Rebellion, Earth, Retaliation, Reckoning) before trying to play MP. You can check what's installed in origin under My game library -> Mass Effect 3 -> Extra Content).

And last but not least a lot of problems are related to the configuration of your internet connection see my post here .

That's about all I could come off the top of my head.