A mixture of good ideas and basic troubleshooting:

Do a clean re-install of Windows. It could be that simple!
If you don't want to re-install Windows, do a clean re-install of your drivers with ATIman, here: http://atiman.go-board.net/
Your RAM might be bad. Run Memtest86+ overnight and make sure the RAM is alright. http://www.memtest.org/
When you mine, do you mine one card at a time (for testing) or all at once? Instead of mining with all cards and causing BSoD, try mining with single cards at a time. See if the 3rd card alone causes the BSoD, or if the 5970's have something to do with it.
Are you using a custom BIOS on any of your cards, by chance? Undervolting/overvolting? Underclocking/overclocking?
Test the 3 cards you intend for this rig in a completely different rig, to make sure that the issue is definitely card related, and not related to motherboard, RAM, hard drive, or PSU.

Hey all

It turns out to have been a bad PCIe extender.

Now have 4x 7970's up and running perfectly happy.....no issues at all.