Well I don't know about the coil whine issues and I am not familiar with that graphics card, but I have taken many apart in my time from low end to ones that costs 900+ bucks. I pulled up a picture of the card and its a standard card design, the screws are normally on the circuit board side and not the plastic side. I would take off all the screws on the that side and if you don't have a good memory mark where they went or take good pictures. If you took off all the right screws the plastic part and the fans should come off very very easy, pretty much fall off. Do not take it off tho, gently lift it like 1/4 of a inch and peek in there to see if there are any connections you need to unplug first before removing. Remove them and take of off, clean the fans with air then alcohol pads to get off the caked on dust. Also do this for the heatsink and regrease it all, clean the thermal pads if they are dust but be careful NOT to tear them they are delicate.
Good luck, for such high end devices I always strap in.....
I do have to add this if ONLY for cards that have been ignored for a very long time, if its a new card just blow dust and skip this long step. This is also great if your card is over heating!