Hmmmph. Well, I guess maybe the problem lies elsewhere then. Which drivers are you running? I'm currently running my 3x 7950 system on Catalyst 12.8 (best performance) but also had it running fine on version 13.1, 13.3beta and 13.6beta.

The 11.78V on the +12V is technically still within spec (+-5%), but sounds a bit low. It's obvious your PSU is under some major stress.
As you said it seems this indeed might not be your only problem though.

I'm going to go with blockzett on this one. Maybe 1.1V isn't enough core voltage for your cards. You could try again with only two cards, but raise their voltage up a little and see what happens. If the 1.1V that you state is inside of Sapphire Trixx, keep in mind that your true voltage will be lower. My 7950s have a vdroop of around 60mV which means that when I set them to 1100mV in Trixx, they actually run at 1040mV as measured by GPU-Z.

Other than this I'm a bit stumped now, sorry.