Picking up something like a 6570 would probably be cheaper than getting a pricey board with more features. Run some displays off the dGPU, and one off the iGPU.
I don't even know if you can run three DVI-type displays off an APU. Given their dedicated cards couldn't until recently, I doubt it (FYI: HDMI uses the same underlying tech as DVI, and counts as DVI-type).