I have 2 7970's, 1 7950, and 1 280x on a 1200 gold rated psu. It should handle them no problem, I tried upping the voltage, and I tried it in both the config file and in msi afterburner with no luck

and yes, all in 16x slots - two 7970's directly connected to mobo, and the others on 16x-16x risers
Heterogeneous card configurations almost always sacrifice performance. Specifically with 3 different types of cards, you're going to be losing at least some hash rate.
Go with Homogeneous card setups (all the same brand and model, preferably the same batch), if you want to really push your machines to the limit.
I've found after a year that pushing my machines to the limit is less productive than a nice stable continuous hash day after day after day. But maybe I suck at this.