My set up is not too dissimilar to yours. I have the GD01 case, Zalman 9500A CPU fan and two 8800GT's in SLI. Getting the balance between fan noise and cooling required some thought.
I used a fan contraoller, installed in a 5.25" bay eg http://www.frozencpu.com/products/10348/bu...l?tl=g34c17s286
You can get 3.5" fan controllers too - I have mine controlling the CPU fan and three case fans.
For case fans I try and use the Enermax magnetic bearing 80mm fans as they are whisper quiet. I drilled some holes in the top of my case and glued one there to suck out hot air. If you don't have enough space you can also use a hard drive fan as they are only 10mm thick.http://www.newegg.com/Product/Product.aspx...N82E16811999199
I also use one of those PCI slot coolers to suck out air from the back of the case. At the front I use two 92mm fans to get as much cool air intothe case as possible. On the side I have one of those 80mm enermax fans blowing cool air onto the CPU heat sink.
I also used some sound proofing padding on the inside of the lid and on the sides where there was space.
It sounds like the bulk of the noise is coming from your 5970 card, here is an excellent report on the heat generation of that card:http://www.behardware.com/articles/747-15/...cteristics.html
I use Rivatuna to control the fan speed on my two cards, not sure if it works on the 5970 but you can use MSI afterburner I think.
Good luck !