After this magically worked, they died again shortly afterwards. I followed the various pieces of advice here and cut a small notch in the rubber tubing door connector (the tubes definitely had water in them). And now my speakers do magically work again. I live in Seattle, so rather than the 24hrs that someone else suggested here, it took a full three weeks before the speakers dried out.I had the same symptoms as those in the original post... no sound from rear speakers, but rear seat audio was not switched on and the fader was set in the middle.
You're going to have to trust me here, but there is a little music symbol on the top right of the head unit (the one that adjusts fader/bass etc). If you hold that down for a few seconds, it will reset each of those fader-style controls to the middle. I did that and suddenly I had rear seat audio. And yes, the fader *was* set in the middle before I did that.
I realise this is far too late for the original poster (and I don't think would help anyway given their update), but I thought I'd add this here because this is the #1 Google hit for "saturn outlook rear speakers stopped working".