So I put in an RMA request last Monday, and received my new one today. Not bad, although it is cross-shipped, so I still need to return the old one.
The new one still sort of "whines", but it is a different sort of noise and the frequency is much less annoying.
Edit: Damn, it is actually still there. Beginning to wonder if it is another component like the mobo or PSU, and the GPU simply triggers it.