As CK says of cgminer, the 7970 requires the memory clock to be no more than -150 than the engine clock. Per the cgminer readme:
--gpu-memdiff -125
This setting will modify the memory speed whenever the GPU clock speed is
modified by --auto-gpu. In this example, it will set the memory speed to
be 125 Mhz lower than the GPU speed. This is useful for some cards like the
6970 which normally don't allow a bigger clock speed difference. The 6970 is
known to only allow -125, while the 7970 only allows -150.
My 6970 runs with a memclock of 110 just fine; I underclock with "aticonfig --odsc=970,110". Trust me, I tried running my 7970s at 300, 500, etc.
I don't have any experience with the Nano Diamond. I've used AS Céramique, which is nice for GPUs cuz it's non-conductive, and pretty decent.
The stuff I've been looking at is non-conductive, so I think it'll be fine.
Also, as another status update, I'm pretty sure that the hot GPU was defective because it shorted. Sparks were flying and everything. I'm honestly surprised (and fortunate) that nothing caught on fire. I've told Gigabytes and will hopefully get a refund.