ASUS HD7970's take triple slots, but Sapphires dont.
That motherboard can support dual cards in Crossfire/SLI, any more than that and you will be limiting them with decreased bandwidth.
You want the 212 EVO, better baseplate with wider contact pipes.
Drop a RAM kit, 32GB is just overkill in a gaming rig, even 16GB is too much. Also its not a good idea to mix RAM kits, even if they have the same specs.
A rig like this deserves a better case. I recommend the HAF-XM.