Hi 
There is a way to achieve this, however as you pointed out there is a limitation to Eyefinity, with a max of 6 monitors, not 4 as you put, and Eyefinity grouping does not work across cards.
There is however a way around this with the use of some additional hardware or software, each with their own limitations, to be able to achieve the 12x video wall you are looking to create.
SOFTWARE:
If you are looking to play games based on DX9 then it is possible to use some software called SoftTH which will allow a vast array of monitors to be used, creating its own sudo Eyefinity grouping across multiple cards, the software is limited but it is a free solution.
Other DX9 based applications may work when rendered in fullscreen mode.
HARDWARE:
You have a W7100 which supports 4x DP1.2 outputs.
Each DP output has enough bandwidth to drive up to 4x 1920x1200@60hz
Using this card, or two of them in Crossfire, you can connect all 12 monitors to a single card using the configuration of hardware below...
Using 2x 2-port MST hubs from the W7100 it is possible to extend the total DP outputs from 4 to 6.
From these 6x DP outputs one may then use the Zotac Dual HDMI adaptors, there is a thread here with more information.
According to BHawthorne it is possible to run the adapters in portrait mode...
BHawthorne wrote: The behavior of the adapter is that on the two 1024x768 projectors I threw on it, it detected up to 2048x768 for the max resolution in the microsoft display control panel. It sees 2048x768 and 1600x600 for dual resolutions. And 1920x1080 down to 800x600 on single resolutions. Single resolutions are cloned to both displays much like how Eyefinity does. When you force portrait mode on it it'll make 2048x768 it into 768x2048 not 1536x1024, so it's treated like a pseudo-single display.
This will allow you to run the 12 monitors natively on a single card as the Zotac dual HDMI adapters are seen as a single monitor each, with further splits the image, so in windows you will technically see 6 monitors, each with a resolution that combines 2 monitors each, and you will be able to setup an Eyefinity configuration accordingly.
Note that only the FirePro range support 6x portrait monitors, consumer Eyefinity cards only allow 5x portrait monitor configurations.
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it's pretty nice !