I wouldn't use a case at all for 4x6950 GPUs on a dedicated miner. There are many innovative caseless solutions on the board. And boot from a 4GB USB stick and go diskless (no HDD or DVD).

With the PCIe entender cables (Cablesuarus.com) mentioned by badfrog this M/B would probably support 6 GPUs as the two PCIe x1 slots will work fine for mining.