Just created an account to thank you for this tutorial. I am waiting on a warranty repair on a 280X and this card is my 'backup' and I started getting the fan lock up issues with it and this worked like a dream. I actually think the fan is better now than it was when it was shipped.
A tip for those using the drill, let the drill do the work with the relatively soft plastic, you don't really need to put any pressure on it other than to hold it in place. Drill at a slowish speed for a second or so each time, clear the debris and see if you can see the shaft. It is like a small pin about 1mm across which moves when the gently pull the fan up from the base. What I did was to pull it slightly so there was a gap and sprayed it with WD40, finger spin as the OP said and it should spin freely for a second or so.