Well the fan sounds damaged. I don't accept things damaged from factory
I have heard rumors that the gigabyte 7870 OC using afterburner can drop to 0%
and it's a brilliant card for what you want. Credit goes to SPCR username:"Wanky" for finding this out. I merely confirmed that he didn't have a weird sample and wasn't brave enough to try another brand. Maybe SPCR can try the afterburner software on the asus and see if it can go down to 0 as well since it was recently reviewed. The other reason SPCR should review the gigabyte 7870 is that they are more flexible in terms of adjusting voltage than the 660/660ti so you can undervolt and reduce temps/noise. On top of that for some reason Gigabyte went all out with a tri fan design for the 7870 and a bigger heatsink. This allows it to cool the card passively at idle. Compare that to Gigabytes implementation of the 660/660ti (2gb). They are smaller heatsinks with dual fans.
I'd definitely love to know also if there is Any way to reduce idle fan speed below the minimum 20 % since I'm looking at a XFX 7970 DD, which is noisy at idle according to reviews.
Google Msi Afterburner and download that. It will allow you to get fan speed to 0%. That doesn't mean that it will turn off. Most fans have a minimum speed so reducing fan speed from 20% to 0% might not do anything at all.